// Numbas version: exam_results_page_options
{"name": "Listar los elementos de los siguientes conjuntos...", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Listar los elementos de los siguientes conjuntos...", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Considere el conjunto universal como $ U = \\var {univ} $ y sean $ A $ y $ B $ subconjuntos de $ U $</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">tales que $ A = \\var {set1} $ y $ B = \\var {set2} $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">El conjunto universal para el producto cartesiano $ A \\times B $ es $ U \\times U $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Listar los elementos de los siguientes conjuntos.</span></span></p>\n<p><strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Indicaciones.</span></span></strong></p>\n<ul>\n<li><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Ingrese los conjuntos en la forma&nbsp; </span></span><strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">set (a, b, c, d),&nbsp; p</span></span></strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">or ejemplo, si ingresa&nbsp; </span></span><strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">set (1,2,3)</span></span></strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\"> &nbsp; se observa el conjunto $ \\{1,2,3 \\} $</span></span><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\"></span></span></li>\n<li><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Un par ordenado $ (a, b) $ del producto cartesiano, se muestra como $ [a, b] $.</span></span></li>\n<li><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Por ejemplo, el conjunto&nbsp; </span></span><strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">set([1,1], [1,2], [2,3])</span></span></strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\"> &nbsp;nos da como resultado $ \\{[1,1], [1,2], [2,3] \\} $</span></span></li>\n<li><span style=\"vertical-align: inherit;\">El conjunto vacio se ingresa como&nbsp; <strong>set ().</strong>&nbsp;<span style=\"vertical-align: inherit;\"></span></span></li>\n</ul>\n<p></p>", "advice": "<h4><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">una)</span></span></h4>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ A ^ c = UA $, es el conjunto de todos los elementos de $ U $ y no est&aacute;n en $ A $, as&iacute; $ A ^ c = \\ var {univ - set1} $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ B ^ c = UB $, es el conjunto de todos los elementos de $ U $ y no est&aacute;n en $ B $, as&iacute; $ B ^ c = \\ var {univ - set1} $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ A ^ c \\ cap B ^ c $, es el conjunto de todos los elementos que se encuentran en $ A ^ c $ y $ B ^ c $.&nbsp;</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Esto es equivalente al conjunto de todos los elementos ni en $ A $ ni en $ B $, es decir, $ \\ var {(univ-set1) y (univ-set2)} $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ A \\ cap B $ Es el conjunto de todos los elementos presentes en $ A $ y $ B $, es decir, $ \\ var {set1 y set2} $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">As&iacute; que $ (A ^ c \\ cap B ^ c) \\ times (A \\ cap B) $ es el conjunto de todos los pares $ (x, y) $, donde $ x $ est&aacute; en $ A ^ c \\ cap B ^ c $, y $ y $ est&aacute; en $ A \\ cap B $.</span></span></p>\n<h4><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">si)</span></span></h4>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ (U \\ times A) ^ c $ es el conjunto de todos los pares $ (x, y) $ que se encuentra en $ U \\ times U $ que no est&aacute;n en $ U \\ times A $. </span><span style=\"vertical-align: inherit;\">Ya que $ U $ es el conjunto universal, esto es equivalente a $ U \\ times (A ^ c) $, el producto de $ U $ con el conjunto de elementos no est&aacute;n en $ A $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Del mismo modo, $ (U \\ times B) ^ c $ es equivalente a $ U \\ times (B ^ c) $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Otra vez, $ U $ es el conjunto universal, $ (U \\ times A) ^ c \\ cap (U \\ times B) ^ c = U \\ times (A ^ c \\ cap B ^ c) $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Por un argumento similar, $ (A \\ times U) ^ c \\ cap (B \\ times U) ^ c = (A ^ c \\ cap B ^ c) \\ times U $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">As&iacute;, $ (U \\ times A) ^ c \\ cap (U \\ times B) ^ c \\ cap (A \\ times U) ^ c \\ cap (B \\ times U) ^ c $ es equivalente a $ (A ^ c \\ cap B ^ c) \\ times (A ^ c \\ cap B ^ c) $. </span><span style=\"vertical-align: inherit;\">Esto es, el conjunto de todos los pares que no est&aacute;n en $ A $ o $ B $.</span></span></p>\n<h4><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">C)</span></span></h4>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ AB $ es el conjunto de elementos que se encuentran en $ A $ pero no $ B $, es decir, $ \\ var {set1-set2} $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ (A \\ cup B) ^ c $ es el conjunto de elementos $ U - (A \\ cup B) $, los problemas est&aacute;n en $ U $ y no est&aacute; $ A \\ cup B $, as&iacute; $ (A \\ cup B ) ^ c = \\ var {univ- (set1 o set2)} $.</span></span></p>\n<h4><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">re)</span></span></h4>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ [(A \\ cup B) \\ times U] ^ c $ es equivalente a $ (A \\ cup B) ^ c \\ times U $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">As&iacute; $ [(A \\ cup B) \\ times U] ^ c \\ cap [U \\ times (A \\ cap B)] = (A \\ cup B) ^ c \\ times (A \\ cap B) $.</span></span></p>\n<h4><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">mi)</span></span></h4>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">$ A ^ cB $ es el conjunto de todos los elementos que se encuentran en $ A ^ c $ pero no $ B $. </span><span style=\"vertical-align: inherit;\">Eso es equivalente al conjunto de elementos que no est&aacute;n en $ A $ ni en $ B $, es decir, $ (A \\ cup B) ^ c = \\ var {univ- (set1 o set2)} $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Del mismo modo, $ B ^ c - A = (B \\ cup A) ^ c = (A \\ cup B) ^ c = \\ var {univ- (set1 o set2)} $.</span></span></p>", 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