tag:blogger.com,1999:blog-15109174658776606992024-03-13T04:48:53.802-07:00CONJUNTOSNANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-1510917465877660699.post-54512793865107748022012-03-11T12:19:00.003-07:002012-03-11T12:20:26.380-07:00INTRODUCCIÓN CONJUNTOS<a href="http://www.slideshare.net/miss_rosy/conjuntos-1172297" target="_blank">CONJUNTOS</a> <br />
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<strong style="display: block; margin: 12px 0 4px;"><a href="http://www.slideshare.net/miss_rosy/conjuntos-1172297" target="_blank" title="Conjuntos">Conjuntos</a></strong> <iframe frameborder="0" height="355" marginheight="0" marginwidth="0" scrolling="no" src="http://www.slideshare.net/slideshow/embed_code/1172297" width="425"></iframe> <br />
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</div>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com0tag:blogger.com,1999:blog-1510917465877660699.post-7964225965922918142012-03-11T12:16:00.002-07:002012-03-11T12:21:28.696-07:00DEFINICION Y NOTACION DE UN CONJUNTO<br />
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<span style="color: navy; font-size: large;">DEFINICION</span></div>
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<span style="color: blue; font-family: Arial, Helvetica, sans-serif;">Sabemos que la palabra conjunto implica la idea de una colección de objetos que se caracterizan en algo común.</span></div>
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<span style="color: blue; font-family: Arial, Helvetica, sans-serif;">En matemática tiene el mismo significado, sólo que a estos objetos se les llama <strong>elementos</strong> o miembros del conjunto.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: blue;">La noción simple de una <strong>colección</strong> o conjunto de objetos es fundamental en la estructura básica de las matemáticas y fue </span><a href="http://sipan.inictel.gob.pe/internet/av/cantor.htm"><span style="color: blue;">Georg Cantor</span></a><span style="color: blue;">, en los años 1870 quien primero llamó la atención de los matemáticos a este respecto.</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: blue;">No puede darse una definición satisfactoria de un conjunto en términos de conceptos simples, por lo tanto la palabra "</span><span style="color: blue;"><em>CONJUNTO</em></span><span style="color: blue;">" debe aceptarse lógicamente como un </span><span style="color: blue;"><em>término no definido</em></span><span style="color: blue;">.</span></span></div>
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<span style="color: blue; font-family: Arial, Helvetica, sans-serif; font-size: small;">Un conjunto es una colección bien definida de objetos de cualquier clase.</span></div>
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<div style="line-height: 19px; margin-bottom: 1em; margin-top: 1em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left;">
<span style="background-color: white;"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span class="keyword" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-weight: bold;">Notación conjunto</span> es una manera de decir cuál está en un conjunto. El conjunto se nombra generalmente con una mayúscula como esto:</span></span></div>
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<span style="background-color: white;"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><var style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-style: normal; white-space: nowrap;">A = {definición del conjunto}</var><sub style="vertical-align: text-bottom;">1</sub></span></span></div>
<span style="background-color: white;"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19px; text-align: left;">La definición del conjunto está dentro de las llaves: </span><var style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-style: normal; text-align: left; white-space: nowrap;">{}</var><span style="line-height: 19px; text-align: left;">. Hay dos estilos de la definición del conjunto que pueden estar en llaves.</span></span></span><br />
<ul style="line-height: 19px; list-style-image: initial; list-style-position: initial; margin-bottom: 0.7em; margin-left: 30px; margin-right: 1em; margin-top: 2px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left;">
<li style="list-style-image: initial; list-style-position: outside; list-style-type: disc; margin-bottom: 0px; margin-left: 7px; margin-right: 17px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span style="background-color: white;"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><b>Lista</b>: Si un conjunto tiene apenas algunos elementos, el conjunto puede ser definido enumerando todos los elementos:</span></span><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: center;">
<span style="background-color: white;"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><var style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-style: normal; white-space: nowrap;">B = {libro, lápiz, borrador}</var><sub style="vertical-align: text-bottom;">2</sub></span></span></div>
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En esta definición, el conjunto <var style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-style: normal; white-space: nowrap;">B</var> tiene tres elementos: libro, lápiz, y borrador.</span></span></li>
<li style="list-style-image: initial; list-style-position: outside; list-style-type: disc; margin-bottom: 0px; margin-left: 7px; margin-right: 17px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span style="background-color: white;"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><b>Regla</b>: Un conjunto se puede definir por una regla. Mientras que esta regla puede simplemente ser una oración por ejemplo <var style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-style: normal; white-space: nowrap;">{El conjunto de toda la roca en mi jardín.}</var>, los símbolos de la matemáticas se utilizan típicamente:</span></span><div class="eqnalone" style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 3em;">
<span style="background-color: white;"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><var style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-style: normal; white-space: nowrap;">C = { x | x <span title="es un elemento de">∈</span> <abbr style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px;" title="número naturale">ℕ</abbr>, x < 20 }</var><sub style="vertical-align: text-bottom;">3</sub></span></span></div>
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Conjunto <var style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-style: normal; white-space: nowrap;">C</var> contiene todos los números naturales menos de 20.</span></span></li>
</ul>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com0tag:blogger.com,1999:blog-1510917465877660699.post-27176201210060872852012-03-11T12:00:00.002-07:002012-03-11T12:11:57.044-07:00REPRESENTACION DE CONJUNTOS<br />
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<tr><td style="border-bottom-color: rgb(153, 153, 153); border-bottom-style: solid; border-bottom-width: 1px; border-right-color: rgb(153, 153, 153); border-right-style: solid; border-right-width: 1px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 2px; padding-left: 10px; padding-right: 10px; padding-top: 2px;"><div align="center" style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<span style="font-size: medium;">Por diagrama de Venn Euler</span><br />
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<span style="font-size: medium;">Entre llaves</span></div>
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<span style="font-size: medium;"><img align="absmiddle" height="105" src="http://www.profesorenlinea.cl/matematica/Conjuntos/image008.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-color: transparent; border-left-width: 0px; border-right-color: transparent; border-right-width: 0px; border-style: initial; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 0px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="320" /></span></div>
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<b><span style="font-size: large;"> </span></b><br />
<b><span style="font-size: large;"> S = {a, e, i, o, u}</span></b><br />
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<b style="background-color: white; text-align: left;"><span style="font-size: large;">R = {1; 2; 3; 4}</span></b><br />
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<b><span style="font-size: medium;">Se escribe una coma (,) </span></b><b style="background-color: white;"><span style="font-size: medium;">o (;) para separar los </span></b></div>
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<b style="background-color: white; text-align: left;"><span style="font-size: medium;"><br /></span></b></div>
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<b style="background-color: white; text-align: left;"><span style="font-size: medium;">elementos.</span></b></div>
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<span style="font-size: medium;"></span></div>
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<b style="background-color: white; font-size: x-large;"><br /></b><br />
<b style="background-color: white; font-size: x-large;">ENTRE LLAVES</b><br />
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<span style="background-color: white; font-size: medium;">Ejemplo: Sean los conjuntos</span><span style="background-color: white; font-size: x-large;"> A={ 1, 3, 5, 7, 9 } </span><br />
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<span style="background-color: white; font-size: x-large;"> B={ 10, 11, 12 }</span></div>
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<span style="font-size: medium;"> </span><span style="font-size: x-large;">Diagrama de venn Euler<b style="background-color: white; line-height: 50px; text-align: left;"> :</b></span></div>
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<span style="font-size: large;"><span style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;">Estos diagramas se usan para mostrar gráficamente la agrupación de </span></span></div>
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<span style="font-size: large;"><span style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;"><br /></span></span></div>
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<span style="font-size: large;"><span style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;">cosas </span><i style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;">elementos</i><span style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;"> en </span><a class="mw-redirect" href="http://es.wikipedia.org/wiki/Conjuntos" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: none; background-origin: initial; color: #0b0080; font-family: sans-serif; line-height: 19px; text-decoration: none;" title="Conjuntos">conjuntos</a><span style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;">, representando cada conjunto mediante un </span></span></div>
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<span style="font-size: large;"><span style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;"><br /></span></span></div>
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<span style="font-size: large;"><span style="background-color: white; color: black; font-family: sans-serif; line-height: 19px;">círculo o un óvalo.</span></span></div>
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<img height="188" src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/63/Venn_diagram_cmyk.png/220px-Venn_diagram_cmyk.png" width="200" /> <img src="http://colposfesz.galeon.com/est501/conjunto/fyv2.gif" style="background-color: white;" /></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com0tag:blogger.com,1999:blog-1510917465877660699.post-14799682703154200352012-03-11T11:59:00.002-07:002012-03-11T12:11:27.259-07:00DETERMINACION DE CONJUNTOS<br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-image: initial; border-left-color: transparent; border-right-color: transparent; border-top-color: transparent; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px;"><span style="font-size: large;"><br class="Apple-interchange-newline" /><img height="27" src="http://sipan.inictel.gob.pe/internet/av/graficos/extension.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="200" /></span></span> </span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Se dice que un conjunto es determinado por <em>extensión</em> (o enumeración), cuando se da una lista que comprende a todos los elementos del conjunto y sólo a ellos.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img height="27" src="http://sipan.inictel.gob.pe/internet/av/graficos/ejemplo.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="97" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">A = { a, e, i, o, u }</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">B = { 0, 2, 4, 6, 8 }</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">C = { c, <img height="9" src="http://sipan.inictel.gob.pe/internet/av/graficos/o.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="8" />, <img height="9" src="http://sipan.inictel.gob.pe/internet/av/graficos/n.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="9" />, j, u, t, s } En un conjunto determinado por extensión no se repite un mismo elemento.</span></div>
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<a href="http://sipan.inictel.gob.pe/internet/av/graficos/comprension.gif" imageanchor="1" style="clear: left; color: #7d3611; float: left; font-family: Georgia, Utopia, 'Palatino Linotype', Palatino, serif; margin-bottom: 1em; margin-right: 1em; text-decoration: none;"><span style="font-size: large;"><img border="0" height="25" src="http://sipan.inictel.gob.pe/internet/av/graficos/comprension.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-color: initial; border-image: initial; border-left-color: transparent; border-left-style: solid; border-right-color: transparent; border-right-style: solid; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-width: initial; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px; position: relative;" width="200" /></span></a><span style="font-family: Arial, Helvetica, sans-serif; font-size: 16px;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Se dice que un conjunto es determinado por <em>comprensión</em>, cuando se da una propiedad que la cumpla en todos los elementos del conjunto y sólo a ellos.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img height="27" src="http://sipan.inictel.gob.pe/internet/av/graficos/ejemplo.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="97" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">A = { x/x es una vocal }</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">B = { x/x es un número par menor que 10 }</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">C = { x/x es una letra de la palabra conjuntos }</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Vamos a mostrarte un cuadro comparativo de determinación de conjuntos</span></div>
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<table border="0" style="background-color: white; color: #4e2800; font-family: Georgia, Utopia, 'Palatino Linotype', Palatino, serif; font-size: 16px; line-height: 22px;"><tbody>
<tr><td><span style="font-family: Arial, Helvetica, sans-serif;"><img height="27" src="http://sipan.inictel.gob.pe/internet/av/graficos/extension.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="200" /> </span></td><td></td><td><span style="font-family: Arial, Helvetica, sans-serif;"><img height="25" src="http://sipan.inictel.gob.pe/internet/av/graficos/comprension.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="200" /></span></td></tr>
<tr><td><span style="font-family: Arial, Helvetica, sans-serif;">A = { a, e, i, o, u }</span></td><td></td><td><span style="font-family: Arial, Helvetica, sans-serif;">A = { x/x es una vocal }</span></td></tr>
<tr><td><span style="font-family: Arial, Helvetica, sans-serif;">B = { 0, 2, 4, 6, 8 }</span></td><td></td><td><span style="font-family: Arial, Helvetica, sans-serif;">B = { x/x es un número par menor que 10 }</span></td></tr>
<tr><td><span style="font-family: Arial, Helvetica, sans-serif;">C = { c, <img height="9" src="http://sipan.inictel.gob.pe/internet/av/graficos/o.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="8" />, <img height="9" src="http://sipan.inictel.gob.pe/internet/av/graficos/n.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="9" />, j, u, t, s }</span></td><td></td><td><span style="font-family: Arial, Helvetica, sans-serif;">C = { x/x es una letra de la palabra conjuntos }</span></td></tr>
<tr><td><span style="font-family: Arial, Helvetica, sans-serif;">D = { 1, 3, 5, 7, 9 }</span></td><td></td><td><span style="font-family: Arial, Helvetica, sans-serif;">D = { x/x es un número impar menor que 10 }</span></td></tr>
<tr><td><span style="font-family: Arial, Helvetica, sans-serif;">E = { b, c, d, f, g, h, j, . . . }</span></td><td></td><td><span style="font-family: Arial, Helvetica, sans-serif;">E = { x/x es una consonante }</span></td></tr>
</tbody></table>
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<br class="Apple-interchange-newline" /></div>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com0tag:blogger.com,1999:blog-1510917465877660699.post-37523685281867833482012-03-11T11:37:00.000-07:002012-03-11T11:37:15.846-07:00PERTENECE, NO PERTENECE<br />
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<span style="color: #38761d; font-family: Impact, sans-serif; font-size: x-large;">¿Pertenece o no pertenece?</span><span style="color: #351c75; font-size: medium;"><o:p></o:p></span></div>
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<span style="font-family: Tahoma, sans-serif;"><span style="font-size: large;">I.<b><u> Lee con atención.</u></b></span></span></div>
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<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"> </span></span><br />
<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;">La relación que se establece entre los <b>elementos</b></span><b style="text-indent: -45.35pt;"><span style="font-family: Tahoma, sans-serif;"> y</span></b></span><br />
<span style="font-size: large;"><b style="text-indent: -45.35pt;"><span style="font-family: Tahoma, sans-serif;">conjuntos</span></b><span style="font-family: Tahoma, sans-serif; text-indent: -45.35pt;"> es de <b><span style="text-transform: uppercase;">PERTENENCIA.</span></b></span></span></div>
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<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"> </span><span style="font-family: Tahoma, sans-serif;"><o:p></o:p></span></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></div>
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<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"> <b> Notación:</b></span><span style="font-family: Tahoma, sans-serif;"><o:p></o:p></span></span></div>
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<span style="font-size: large;"><br /></span><br />
<ul style="line-height: 1.4; list-style-image: initial; list-style-position: initial; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 2.5em; padding-right: 2.5em; padding-top: 0px;">
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"> Si el elemento <b>"pertenece"</b> al conjuto: </span><b><span style="color: red; font-family: Symbol;">Î</span></b></span></li>
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"> Si el elemento <b>"no pertenece" </b>al conjunto: </span><span style="color: #cc0000; font-family: Symbol;"><b>Ï</b></span></span></li>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;">Ejemplo : Observando los siguientes conjuntos.</span></div>
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<div style="font-family: Georgia, Utopia, 'Palatino Linotype', Palatino, serif; line-height: 20pt;">
<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"><br /></span></span></div>
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<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;">P = {2; 4; 6; 8; 10} </span><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> </span></span><span style="background-color: white; font-family: Tahoma, sans-serif; font-size: large; line-height: 20px;">Q = {1; 3; 5; 7; 9; 11; 13}</span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large; line-height: 20px;"><br /></span><br />
<span style="font-family: Tahoma, sans-serif; font-size: large; line-height: 20px;">Podemos afirmar:</span><br />
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<span style="font-size: large;"><span lang="EN-US" style="font-family: Tahoma, sans-serif;"> 5</span><b><span style="color: red; font-family: Symbol;">Ï</span></b><span style="font-family: Tahoma, sans-serif;">P 12</span><b><span style="color: red; font-family: Symbol;">Î</span></b><span style="font-family: Tahoma, sans-serif;">Q </span><span style="font-family: Tahoma, sans-serif;">14</span><b><span style="color: red; font-family: Symbol;">Ï</span></b><span style="font-family: Tahoma, sans-serif;">Q </span></span><br />
<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"> 6</span><b><span style="color: red; font-family: Symbol;">Î</span></b><span style="font-family: Tahoma, sans-serif;"> P </span><span lang="EN-US" style="font-family: Tahoma, sans-serif;"> 8<b style="font-family: 'Times New Roman';"><span style="color: red; font-family: Symbol;">Î</span></b> P 8 </span><b><span style="color: red; font-family: Symbol;">Ï</span></b><span style="font-family: Tahoma, sans-serif;"> Q </span></span></div>
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<span style="font-size: large;"><span lang="EN-US" style="font-family: Tahoma, sans-serif;"> </span><span style="font-family: Tahoma, sans-serif;"> </span></span></div>
<span style="font-family: Impact, sans-serif; font-size: large; text-align: center;">Relación entre conjuntos</span></div>
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<span style="font-size: large;"><br /></span></div>
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<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;">I. <u><b>Lee con atención:</b></u></span><span style="font-family: Tahoma, sans-serif;"><o:p></o:p></span></span><br />
<span style="font-family: Tahoma, sans-serif; font-size: large;"><u><b><br /></b></u></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></div>
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<span style="font-size: large;"><span style="position: relative; z-index: 251657725;"><span style="height: 64px; left: 47px; position: absolute; top: -1px; width: 547px;"></span><span style="height: 64px; left: 47px; position: absolute; top: -1px; width: 547px;"><br /></span><span style="height: 64px; left: 47px; position: absolute; top: -1px; width: 547px;"><br /></span></span><span style="font-family: Tahoma, sans-serif;"> Decimos que el conjunto B es subconjunto del conjunto A, cuando todos </span><span style="font-family: Tahoma, sans-serif; line-height: 20pt;">los elementos de B son elementos de A. En ese caso B está incluido en A.</span></span><br />
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<span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></div>
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<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;"> La notación de un subconjunto es:</span><span style="font-family: Tahoma, sans-serif;"><o:p></o:p></span></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"> </span><br />
<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;">"Si es subconjunto": </span><span style="font-family: Symbol;"><b><span style="color: red;">Ì</span> (</b></span><span style="font-family: Georgia, 'Times New Roman', serif; font-weight: bold;">Incluido)</span></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"> </span><br />
<span style="font-size: large;"><span style="font-family: Tahoma, sans-serif;">"Si no es subconjunto": </span><b><span style="font-family: Symbol;"><span style="color: red;">Ë</span> </span><span style="font-family: Tahoma, sans-serif;">(No incluido)</span></b></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></div>
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<span style="font-family: Tahoma, sans-serif; font-size: large;"> </span><br />
<span style="font-family: Tahoma, sans-serif; font-size: large;"> Por ejemplo: </span><br />
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<img height="300" src="http://dieumsnh.qfb.umich.mx/matematicas/tc.htm39.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-bottom-style: solid; border-bottom-width: 1px; border-image: initial; border-left-color: transparent; border-left-style: solid; border-left-width: 1px; border-right-color: transparent; border-right-style: solid; border-right-width: 1px; border-top-color: transparent; border-top-left-radius: 0px; border-top-right-radius: 0px; border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.199219) 0px 0px 0px; padding-bottom: 8px; padding-left: 8px; padding-right: 8px; padding-top: 8px;" width="400" /></div>
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<span style="font-family: Tahoma, sans-serif; line-height: 20pt;"><b> <span style="font-size: medium;"> B </span></b></span><b style="line-height: 20pt;"><span style="font-size: medium;"><span style="color: red; font-family: Symbol;">Ì</span><span style="font-family: Tahoma, sans-serif;"> A, se lee: "B está incluido en A" </span></span></b></div>
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<span style="font-size: medium;"><b style="line-height: 20pt;"><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> </span></b><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> </span><b><span style="font-family: Tahoma, sans-serif; line-height: 20pt;">A </span><span style="background-color: white; line-height: 20pt;"><span style="color: red; font-family: Symbol;">Ë</span></span><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> B, se lee: "A no está incluido en B"</span></b></span></div>
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<span style="font-family: Tahoma, sans-serif;"> </span><b><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> </span></b><b style="line-height: 20pt;"><span style="font-family: Tahoma, sans-serif;"> <span style="font-size: medium;"> P</span></span></b><b><span style="font-size: medium;"><span style="line-height: 20pt;"><span style="font-family: Symbol;"><span style="color: red;">Ì</span> B</span></span><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> , se lee: "P está incluido en B" </span><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> </span></span></b></div>
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<b><span style="font-size: medium;"><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"></span><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> C </span><span style="line-height: 20pt;"><span style="color: red; font-family: Symbol;">Ë</span></span><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> B, se lee: "C no está incluido en B"</span></span></b></div>
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<span style="font-family: Tahoma, sans-serif;"><br /></span></div>
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<span style="height: 133px; left: 0px; margin-left: 440px; margin-top: 23px; position: absolute; width: 136px; z-index: 251656704;"></span><span style="font-family: Tahoma, sans-serif;"><o:p></o:p></span></div>
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<span style="font-family: Tahoma, sans-serif;"> <b><span style="font-size: large;">Recuerda:</span></b></span><b><span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></b></div>
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<b><span style="font-family: Tahoma, sans-serif; font-size: large;"><o:p></o:p></span></b></div>
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<span style="font-size: large;"><br /></span><br />
<ul style="line-height: 1.4; list-style-image: initial; list-style-position: initial; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 2.5em; padding-right: 2.5em; padding-top: 0px;">
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="font-size: large;"><span style="font-family: Tahoma, sans-serif; line-height: 20pt;">La relación elemento-conjunto es: </span><b style="line-height: 20pt;"><span style="font-family: Symbol;">Î</span></b><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> o </span><b style="line-height: 20pt;"><span style="font-family: Symbol;">Ï</span></b><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> </span></span></li>
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="font-size: large;"><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> La relación conjunto-conjunto es: </span><b style="line-height: 20pt;"><span style="font-family: Symbol;">Ì</span></b><span style="font-family: Tahoma, sans-serif; line-height: 20pt;"> o </span></span></li>
</ul>
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<ul style="background-color: white; color: #4e2800; font-family: Georgia, Utopia, 'Palatino Linotype', Palatino, serif; line-height: 22px; list-style-image: initial; list-style-position: initial; margin-bottom: 0.5em; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 2.5em; padding-right: 2.5em; padding-top: 0px;">
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="background-color: white; color: #b45f06; font-size: large;"><b>De acuerdo a la definición de inclusión, pueden darse los siguientes casos:</b></span></li>
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="background-color: white; color: #b45f06; font-size: large;"><b> Inclusión del conjunto vacío: El conjunto vacío está incluído en todo conjunto.</b></span></li>
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="background-color: white; color: #b45f06; font-size: large;"><b> Inclusión estricta: Si existe algún elemento de B que no pertenece A.</b></span></li>
<li style="border-bottom-style: none; border-color: initial; border-image: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0.25em; padding-left: 0px; padding-right: 0px; padding-top: 0.25em;"><span style="background-color: white; color: #b45f06; font-size: large;"><b> Inclusión doble: Si todos los elementos de B pertenecen a A. También se llama doble inclusión o igualdad de conjuntos.</b></span></li>
</ul>
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<br class="Apple-interchange-newline" /></div>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com10tag:blogger.com,1999:blog-1510917465877660699.post-69835759573622728672012-03-11T11:20:00.000-07:002012-03-11T11:20:21.083-07:00UNIÓN DE CONJUNTOS<br />
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<span style="color: #0000a0; font-size: large;">UNIÓN DE CONJUNTOS</span></div>
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<span style="color: #0000a0; font-size: large;"><br /></span></div>
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<span style="color: blue; font-size: medium;">La unión de los conjuntos A y B es el conjunto formado por todos los elementos que pertenecen a A o a B o a ambos. Se denota: A U B. La unión de conjuntos se define como:</span></div>
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<span style="color: blue; font-size: medium;">A U B = {x / x <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/pertenece.gif" width="11" /> A o x <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/pertenece.gif" width="11" /> B}</span></div>
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<span style="color: blue; font-size: medium;">En forma gráfica:</span></div>
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<span style="color: blue; font-size: medium;"><img alt="Observa la representación gráfica de la unión" height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="18" src="http://sipan.inictel.gob.pe/internet/av/graficos/grafico.gif" width="336" /></span></div>
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<tr><td><div align="left">
<img align="left" height="75" hspace="0" src="http://sipan.inictel.gob.pe/internet/av/graficos/union1.gif" width="126" /></div>
</td><td> </td><td> </td><td><div align="left">
<img align="left" height="75" hspace="0" src="http://sipan.inictel.gob.pe/internet/av/graficos/union3.gif" width="100" /></div>
</td><td> </td><td><div align="left">
<img align="left" height="123" hspace="0" src="http://sipan.inictel.gob.pe/internet/av/graficos/union4.gif" width="121" /></div>
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<tr><td><span style="color: blue; font-size: medium;"><em>Cuando no tienen</em></span></td><td> </td><td> </td><td><span style="color: blue; font-size: medium;">Cuando tienen algunos</span></td><td> </td><td><span style="color: blue; font-family: Georgia; font-size: medium;">Cuando todos los elementos de un</span></td></tr>
<tr><td><span style="color: blue; font-size: medium;"><em>elementos comunes</em></span></td><td> </td><td> </td><td><span style="color: blue; font-size: medium;">elementos comunes</span></td><td> </td><td><span style="color: blue; font-family: Georgia; font-size: medium;">conjunto pertenecen a otro conjunto</span></td></tr>
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<img alt="Observa los 3 ejemplos siguientes" height="27" src="http://sipan.inictel.gob.pe/internet/av/graficos/ejemplo.gif" width="97" /></div>
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<span style="color: red;"><strong>1. </strong></span><span style="color: black;"><strong>Dados los conjuntos</strong></span><span style="color: red;"><strong>: A = { 0, 1, 2, 3, 4, 5 }, </strong></span><span style="color: green;"><strong>B = { 0, 2, 4 } </strong></span><span style="color: black;"><strong>y</strong></span><span style="color: red;"><strong> </strong></span><span style="color: #0000a0;"><strong>C = { 5, 6, 8 }</strong></span><span style="color: red;"><strong>, </strong></span><span style="color: black;"><strong>efectuar y construir los diagramas respectivos:</strong></span></div>
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<tr><td><span style="color: red;"><strong>a)</strong></span></td><td><span style="color: black;"><strong>A U C</strong></span></td><td> </td><td> </td><td> </td><td> </td><td> </td><td><span style="color: red;"><strong>b)</strong></span></td><td><span style="color: black;"><strong>B U C</strong></span></td><td> </td><td> </td><td> </td><td> </td><td> </td><td><span style="color: red;"><strong>c)</strong></span></td><td><span style="color: black;"><strong>A U B</strong></span></td></tr>
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<strong>Tenemos:</strong></div>
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<strong><img alt="Observa el ejemplo a" height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></strong></div>
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<span style="color: red;">a) <strong>A = { 0, 1, 2, 3, 4, 5 }</strong> </span><span style="color: black;">y</span><span style="color: red;"> </span><span style="color: #0000a0;"><strong>C = { 5, 6, 8 }</strong></span></div>
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<tr><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td><span style="color: black;"><strong>A U C</strong></span><span style="color: red;"><strong> =</strong> { <strong>0, 1, 2, 3, 4</strong>, <strong><img height="11" src="http://sipan.inictel.gob.pe/internet/av/graficos/cincou.gif" width="6" /></strong>, </span><span style="color: #0000a0;"><strong>6, 8</strong></span><span style="color: red;"> }</span></td></tr>
<tr><td><img height="126" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1au.gif" width="227" /></td><td> </td><td> </td><td> </td><td> </td><td> </td><td><img height="126" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1au1.gif" width="184" /></td></tr>
<tr><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td><strong>Representación gráfica de la unión de conjuntos A y C</strong></td></tr>
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<img alt="Observa el ejemplo b" height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></div>
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<span style="color: red;">b) </span><span style="color: green;"><strong>B = { 0, 2, 4 }</strong> </span><span style="color: black;">y</span><span style="color: #0000a0;"> <strong>C = { 5, 6, 8 }</strong></span></div>
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<tr><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td><span style="color: black;"><strong>B U C</strong></span><span style="color: red;"><strong> = { </strong></span><span style="color: green;"><strong>0, 2, 4</strong></span><span style="color: red;"><strong>, </strong></span><span style="color: #0000a0;"><strong>5, 6, 8 </strong></span><span style="color: red;"><strong>}</strong></span></td></tr>
<tr><td><img height="110" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1bu.gif" width="192" /></td><td> </td><td> </td><td> </td><td> </td><td> </td><td><img height="110" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1bu1.gif" width="192" /></td></tr>
<tr><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td><strong>Representación gráfica de la unión de conjuntos B y C</strong></td></tr>
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<img alt="Observa el ejemplo c" height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></div>
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<span style="color: red;">c) <strong>A = { 0, 1, 2, 3, 4, 5 }</strong> </span><span style="color: black;">y</span><span style="color: red;"> </span><span style="color: green;"><strong>B = { 0, 2, 4 }</strong></span></div>
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<tr><td> </td><td> </td><td> </td><td> </td><td><span style="color: black;"><strong>A U B</strong></span><span style="color: red;"><strong> = { <img height="11" src="http://sipan.inictel.gob.pe/internet/av/graficos/cerou.gif" width="6" />, 1, <img height="11" src="http://sipan.inictel.gob.pe/internet/av/graficos/dosu.gif" width="6" />, 3, <img height="11" src="http://sipan.inictel.gob.pe/internet/av/graficos/cuatrou.gif" width="7" />, 5 }</strong></span></td></tr>
<tr><td><img height="133" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1cu.gif" width="218" /></td><td> </td><td> </td><td> </td><td><img height="135" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1cu1.gif" width="115" /></td></tr>
<tr><td> </td><td> </td><td> </td><td> </td><td><strong>Representación gráfica de la unión de conjuntos A y B</strong></td></tr>
</tbody></table>
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<br /></div>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com0tag:blogger.com,1999:blog-1510917465877660699.post-51760068477659582712012-03-11T11:19:00.000-07:002012-03-11T11:19:04.858-07:00INTERSECCIÓN DE CONJUNTO<br />
<div align="center" style="background-color: white;">
<span style="color: #0000a0; font-size: large;">INTERSECCIÓN DE CONJUNTO</span></div>
<div align="center" style="background-color: white;">
<span style="color: #0000a0; font-size: large;"><br /></span></div>
<div align="left" style="background-color: white;">
<span style="color: blue; font-size: medium;">Se define la intersección de dos conjuntos A y B al conjunto de elementos que son comunes a A y B. Se denota por A <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> B, que se lee: A intersección B. La intersección de A y B también se puede definir:</span></div>
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<span style="color: blue; font-size: medium;">A <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> B = { x / x <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/pertenece.gif" width="11" /> A y x <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/pertenece.gif" width="11" /> B } y mediante un diagrama de Venn-Euler:</span></div>
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<img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="18" src="http://sipan.inictel.gob.pe/internet/av/graficos/grafico.gif" width="336" /></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td><img height="85" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion1.gif" width="103" /></td><td> </td><td> </td><td> </td><td><img height="76" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion2.gif" width="126" /></td><td> </td><td> </td><td> </td><td><img height="119" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion3.gif" width="122" /></td></tr>
<tr><td><span style="color: blue; font-size: medium;"><em>Cuando tienen</em></span></td><td> </td><td> </td><td> </td><td><span style="color: blue; font-size: medium;">Cuando no tienen</span></td><td> </td><td> </td><td> </td><td><span style="color: blue; font-family: Georgia; font-size: medium;">Cuando todos los elementos de un</span></td></tr>
<tr><td><span style="color: blue; font-size: medium;"><em>elementos comunes</em></span></td><td> </td><td> </td><td> </td><td><span style="color: blue; font-size: medium;">elementos comunes</span></td><td> </td><td> </td><td> </td><td><span style="color: blue; font-family: Georgia; font-size: medium;">conjunto pertenecen a otro conjunto</span></td></tr>
</tbody></table>
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<img height="27" src="http://sipan.inictel.gob.pe/internet/av/graficos/ejemplo.gif" width="97" /></div>
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<span style="color: red;"><strong>1. </strong></span><span style="color: black;"><strong>Dados los conjuntos</strong></span><span style="color: red;"><strong>: A = { 0, 1, 2, 3, 4, 5 }, </strong></span><span style="color: green;"><strong>B = { 3, 5, 7 } </strong></span><span style="color: black;"><strong>y</strong></span><span style="color: red;"><strong> </strong></span><span style="color: #0000a0;"><strong>C = { 2, 4 }</strong></span><span style="color: red;"><strong>, </strong></span><span style="color: black;"><strong>efectuar y construir los diagramas respectivos:</strong></span></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td><span style="color: red;"><strong>a)</strong></span></td><td><span style="color: black;"><strong>A <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> C</strong></span></td><td> </td><td> </td><td> </td><td> </td><td> </td><td><span style="color: red;"><strong>b)</strong></span></td><td><span style="color: black;"><strong>B <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> C</strong></span></td><td> </td><td> </td><td> </td><td> </td><td> </td><td><span style="color: red;"><strong>c)</strong></span></td><td><span style="color: black;"><strong>A <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> B</strong></span></td></tr>
</tbody></table>
<div align="left" style="background-color: white;">
<strong>Tenemos:</strong></div>
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<strong><img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></strong></div>
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<span style="color: red;">a) <strong>A = { 0, 1, 2, 3, 4, 5 }</strong> </span><span style="color: black;">y</span><span style="color: red;"> </span><span style="color: #0000a0;"><strong>C = { 2, 4 }</strong></span></div>
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<tr><td> </td><td> </td><td> </td><td> </td><td><span style="color: black;"><strong>A <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> C = {</strong></span><span style="color: red;"><strong> <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/dosi.gif" width="8" />, <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/cuatroi.gif" width="8" /> </strong></span><span style="color: black;"><strong>}</strong></span></td></tr>
<tr><td><img height="118" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1ai.gif" width="217" /></td><td> </td><td> </td><td> </td><td><img height="119" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1ai2.gif" width="111" /></td></tr>
<tr><td> </td><td> </td><td> </td><td> </td><td><strong>Representación gráfica de la intersección de conjuntos A y C</strong></td></tr>
</tbody></table>
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<img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></div>
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<span style="color: red;">b) </span><span style="color: green;"><strong>B = { 3, 5, 7 }</strong></span><span style="color: black;"> y</span><span style="color: #0000a0;"> <strong>C = { 2, 4 }</strong></span></div>
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<tr><td> </td><td> </td><td> </td><td> </td><td><span style="color: black;"><strong>B <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> C = {</strong></span><span style="color: red;"><strong> </strong></span><span style="color: black;"><strong>}</strong></span></td></tr>
<tr><td><img height="110" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1bi.gif" width="197" /></td><td> </td><td> </td><td> </td><td><img height="110" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1bi2.gif" width="197" /></td></tr>
<tr><td> </td><td> </td><td> </td><td> </td><td><strong>Representación gráfica de la intersección de conjuntos B y C</strong></td></tr>
</tbody></table>
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<img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></div>
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<span style="color: red;">c)<strong> A = { 0, 1, 2, 3, 4, 5 }</strong> </span><span style="color: black;">y</span><span style="color: red;"> </span><span style="color: green;"><strong>B = { 3, 5, 7 }</strong></span></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td> </td><td> </td><td> </td><td> </td><td><span style="color: black;"><strong>A <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/interseccion.gif" width="8" /> B = {</strong></span><span style="color: red;"><strong> <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/tresi.gif" width="8" />, <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/cincoi.gif" width="8" /> </strong></span><span style="color: black;"><strong>}</strong></span></td></tr>
<tr><td><img height="129" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1ci.gif" width="221" /></td><td> </td><td> </td><td> </td><td><img height="129" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1ci2.gif" width="181" /></td></tr>
<tr><td> </td><td> </td><td> </td><td> </td><td><strong>Representación gráfica de la intersección de conjuntos A y B</strong></td></tr>
</tbody></table>
<div align="left" style="background-color: white;">
<br /></div>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com0tag:blogger.com,1999:blog-1510917465877660699.post-42484118672339832132012-03-11T11:16:00.001-07:002012-04-01T12:07:43.064-07:00DIFERENCIA DE CONJUNTOS<br />
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<span style="color: #004080; font-size: large;">DIFERENCIA DE CONJUNTOS</span><br />
<span style="color: #004080; font-size: large;"><br /></span></div>
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<span style="color: blue; font-size: medium;">Se denomina diferencia de dos conjuntos A y B al conjunto formado por todos los elementos de A pero que no pertenecen a B.</span></div>
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<span style="color: blue; font-size: medium;">La diferencia se denota por: A - B que se lee: A diferencia B o A menos B. Se define la diferencia de dos conjuntos también como:</span></div>
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<span style="color: blue; font-size: medium;">A - B = {x / x <img height="12" src="http://sipan.inictel.gob.pe/internet/av/graficos/pertenece.gif" width="11" /> A y x <img height="18" src="http://sipan.inictel.gob.pe/internet/av/graficos/nopertenece.gif" width="11" /> B}</span></div>
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<span style="color: blue; font-size: medium;">Mediante un diagrama de Venn - Euler:</span></div>
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<img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="18" src="http://sipan.inictel.gob.pe/internet/av/graficos/grafico.gif" width="336" /></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td><img height="96" src="http://sipan.inictel.gob.pe/internet/av/graficos/diferencia1.gif" width="150" /></td><td></td><td><img height="85" src="http://sipan.inictel.gob.pe/internet/av/graficos/diferencia2.gif" width="144" /></td><td></td><td><img height="112" src="http://sipan.inictel.gob.pe/internet/av/graficos/diferencia3.gif" width="94" /></td></tr>
<tr><td><span style="color: blue; font-size: medium;"><em>Cuando no tienen</em></span></td><td></td><td><span style="color: blue; font-size: medium;">Cuando tienen</span></td><td></td><td><span style="color: blue; font-family: Georgia; font-size: medium;">Cuando todos los elementos de un</span></td></tr>
<tr><td><span style="color: blue; font-size: medium;"><em>elementos comunes</em></span></td><td></td><td><span style="color: blue; font-size: medium;">elementos comunes</span></td><td></td><td><span style="color: blue; font-family: Georgia; font-size: medium;">conjunto pertenecen a otro conjunto</span></td></tr>
</tbody></table>
<div align="left" style="background-color: white;">
<img height="27" src="http://sipan.inictel.gob.pe/internet/av/graficos/ejemplo.gif" width="97" /></div>
<div align="left" style="background-color: white;">
<span style="color: red;"><strong>1. </strong></span><span style="color: black;"><strong>Dados los conjuntos</strong></span><span style="color: red;"><strong>: A = { a, b, c, d, e }, </strong></span><span style="color: green;"><strong>B = { a, e } </strong></span><span style="color: black;"><strong>y</strong></span><span style="color: red;"><strong> </strong></span><span style="color: #0000a0;"><strong>C = { d, f, g }</strong></span><span style="color: red;"><strong>, </strong></span><span style="color: black;"><strong>efectuar y construir los diagramas respectivos:</strong></span></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td><span style="color: red;"><strong>a)</strong></span></td><td><span style="color: black;"><strong>A</strong></span><span style="color: black; font-size: large;"><strong> -</strong></span><span style="color: black;"><strong> C</strong></span></td><td></td><td></td><td></td><td></td><td></td><td><span style="color: red;"><strong>b)</strong></span></td><td><span style="color: black;"><strong>B</strong></span><span style="color: black; font-size: large;"><strong> - </strong></span><span style="color: black;"><strong>C</strong></span></td><td></td><td></td><td></td><td></td><td></td><td><span style="color: red;"><strong>c)</strong></span></td><td><span style="color: black;"><strong>A</strong></span><span style="color: black; font-size: large;"><strong> -</strong></span><span style="color: black;"><strong> B</strong></span></td></tr>
</tbody></table>
<div align="left" style="background-color: white;">
<strong>Tenemos:</strong></div>
<div align="left" style="background-color: white;">
<img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></div>
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<span style="color: red;">a) <strong>A = { a, b, c, d, e } </strong></span><span style="color: black;"><strong>y</strong></span><span style="color: red;"><strong> </strong></span><span style="color: #0000a0;"><strong>C = { d, f, g }</strong></span></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td></td><td></td><td></td><td></td><td><span style="color: black;"><strong>A </strong></span><span style="color: black; font-size: large;"><strong>-</strong></span><span style="color: black;"><strong> C </strong></span><span style="color: black; font-size: medium;"><strong>=</strong></span><span style="color: black;"><strong> { </strong></span><span style="color: red; font-size: medium;"><strong>a, b, c, e </strong></span><span style="color: black;"><strong>}</strong></span></td></tr>
<tr><td><img height="94" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1ad.gif" width="176" /></td><td></td><td></td><td></td><td><img height="94" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1ad2.gif" width="140" /></td></tr>
<tr><td></td><td></td><td></td><td></td><td><strong>Representación gráfica de la diferencia de conjuntos A y C</strong></td></tr>
</tbody></table>
<div align="left" style="background-color: white;">
<span style="color: #0000a0;"><strong><img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></strong></span></div>
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<span style="color: red;"><strong>b) </strong></span><span style="color: green;"><strong>B = { a, e } </strong></span><span style="color: black;"><strong>y</strong></span><span style="color: red;"><strong> </strong></span><span style="color: #0000a0;"><strong>C = { d, f, g }</strong></span></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td></td><td></td><td></td><td></td><td><span style="color: black;"><strong>B </strong></span><span style="color: black; font-size: large;"><strong>-</strong></span><span style="color: black;"><strong> C </strong></span><span style="color: black; font-size: medium;"><strong>=</strong></span><span style="color: black;"><strong> { </strong></span><span style="color: green; font-size: medium;"><strong>a, e </strong></span><span style="color: black;"><strong>}</strong></span></td></tr>
<tr><td><img height="93" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1bd.gif" width="160" /></td><td></td><td></td><td></td><td><img height="93" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1bd2.gif" width="160" /></td></tr>
<tr><td></td><td></td><td></td><td></td><td><strong>Representación gráfica de la diferencia de conjuntos B y C</strong></td></tr>
</tbody></table>
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<span style="color: #0000a0;"><strong><img height="49" src="http://sipan.inictel.gob.pe/internet/av/graficos/logoav.gif" width="49" /><img height="19" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej.gif" width="214" /></strong></span></div>
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<span style="color: red;"><strong>c) A = { a, b, c, d, e } </strong></span><span style="color: black;"><strong>y</strong></span><span style="color: red;"><strong> </strong></span><span style="color: green;"><strong>B = { a, e }</strong></span></div>
<table border="0" style="background-color: white;"><tbody>
<tr><td></td><td></td><td></td><td></td><td><span style="color: black;"><strong>A </strong></span><span style="color: black; font-size: large;"><strong>-</strong></span><span style="color: black;"><strong> B </strong></span><span style="color: black; font-size: medium;"><strong>=</strong></span><span style="color: black;"><strong> { </strong></span><span style="color: red; font-size: medium;"><strong>b, c, d </strong></span><span style="color: black;"><strong>}</strong></span></td></tr>
<tr><td><img height="106" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1cd.gif" width="200" /></td><td></td><td></td><td></td><td><img height="113" src="http://sipan.inictel.gob.pe/internet/av/graficos/ej1cd2.gif" width="109" /></td></tr>
<tr><td></td><td></td><td></td><td></td><td><strong>Representación gráfica de la diferencia de conjuntos A y B</strong></td></tr>
</tbody></table>
<br /><br /><br /><ul>
<li><span style="background-color: white; color: red; font-size: x-large;">LA DIFERENCIA A - B</span> </li>
</ul>
<br /><img alt="co_021d2 (4K)" src="http://yachay.stormpages.com/02con/co_021d2.gif" /> <div>
<br /></div>
<div>
<span style="background-color: white;">Gráficamente esta área cubre la superficie QUE A NO COMPARTE CON B.</span></div>
<div>
<ul>
<li><span style="background-color: white; color: red; font-size: x-large;">LA DIFERENCIA B - A</span></li>
</ul>
</div>
<div>
<br style="background-color: white;" /><img alt="co_021d2 (4K)" height="215" src="http://yachay.stormpages.com/02con/co_021d2.gif" style="background-color: white;" width="346" /><span style="background-color: white;"></span><div style="background-color: white;">
Gráficamente esta área cubre la superficie QUE B NO COMPARTE CON A.</div>
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</div>NANCY PILAR CORREA P.http://www.blogger.com/profile/17333963631578190795noreply@blogger.com1