// Numbas version: finer_feedback_settings
{"name": "Enumerar los elementos de un producto cartesiano ...", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Enumerar los elementos de un producto cartesiano ...", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Considere los siguientes conjuntos : $A=\\var{set1}$,&nbsp; $B=\\var{set2}$,&nbsp; $C=\\var{set4}$ y $D=\\var{set5}$.</p>\n<p>Listar los elementos de los siguientes conjuntos.</p>\n<p></p>\n<p><strong>Indicaciones.&nbsp;&nbsp;</strong>Ingrese los conjuntos en la forma <strong>set(a,b,c,d),&nbsp; </strong>por ejemplo, si ingresa&nbsp;<strong>set(1,2,3)</strong>&nbsp; se observa el conjunto&nbsp;$\\{1,2,3\\}$</p>\n<p>Un par ordenado $(a,b)$ del producto cartesiano, es representado como $[a,b]$.</p>\n<p>Por ejemplo,&nbsp; el conjunto&nbsp;<strong>set([1,1],[1,2],[2,3])</strong> nos da como resultado&nbsp;$\\{[1,1], [1,2], [2,3]\\}$.</p>\n<p>El conjunto vac&iacute;o se ingresa como <strong>set().</strong>&nbsp;</p>", "advice": "<h4>a)</h4>\n<p>$A \\times B$ es el conjunto de todos los pares $(a,b)$, donde $a \\in A$ y $b \\in B$.</p>\n<h4>b)</h4>\n<p>$B \\cap D$ es el conjunto de todos los elementos presentes en ambos conjuntos $B$ y $D$, i.e. $\\var{set2 and set5}$.</p>\n<p>$A \\cap C$ es el conjunto de todos los elementos presentes en ambos conjuntos $A$ y $C$, i.e. $\\var{set1 and set4}$.</p>\n<p>$(B\\cap D)\\times (A\\cap C)$ es el conjunto de todos los pares $(x,y)$, donde $x \\in B \\cap D$ y $y \\in A \\cap C$.</p>\n<h4>c)</h4>\n<p>$(A\\cap C)\\times (A\\cap C)\\times (C\\cap D)$ es el conjunto de todos los triples $(x,y,z)$, donde $x \\in A \\cap C$, $y \\in A \\cap C$ y $z \\in C \\cap D$. Observe que $x$ e $y$ no tienen que ser diferente.</p>\n<h4>d)</h4>\n<p>$A-C$ es el conjunto de todos los elementos presentes en $A$ pero no en $C$, i.e. $\\var{set1-set4}$.</p>\n<p>$C-A$ es el conjunto de todos los elementos presentes en$C$ pero no $A$, i.e. $\\var{set4-set1}$.</p>\n<p>$(A-C) \\cup (C-A)$&nbsp; es el conjunto de todos los elementos que est&aacute;n en $A-C$, o en &nbsp;$C-A$, as&iacute; $(A-C) \\cup (C-A) = \\var{(set1-set4) or (set4-set1)}$.</p>\n<h4>e)</h4>\n<p>$(A \\times D)$ es el conjunto de todos los pares $(a,d)$, con $a \\in A$ y $d \\in D$,&nbsp;i.e. $\\var{set(product(list(set1),list(set5)))}$.</p>\n<p>$(C \\times B)$ es el conjunto de todos los pares $(c,b)$, con $c \\in C$ y $b \\in B$, i.e. $\\var{set(product(list(set4),list(set2)))}$.</p>\n<p>$(A \\times D) \\cap (C \\times B)$ es el conjunto de todos los pares presente en&nbsp; los conjuntos anteriores.</p>\n<h4>f)</h4>\n<p>$C \\cap D$ es el conjunto de todos los elementos en ambos conjuntos $C$ y en $D$, as&iacute; $C \\cap D = \\var{set4 and set5}$.</p>\n<p>$C - D$ es el conjunto de todos los elementos que est&aacute;n $C$ y no en $D$, as&iacute; $C-D = \\var{set4 - set5}$.</p>\n<p>$(C \\cap D) \\times (C - D)$ es el conjunto de todos los pares $(x,y)$, donde $x$ est&aacute; en $C \\cap D$&nbsp; e $y$ est&aacute; en $C - D$, as&iacute; $C \\cap D) \\times (C-D) = \\var{set(product(list(set4 and set5),list(set4 - set5)))}$.</p>\n<p>En forma similar, $(D - C) \\times (C \\cap D) = \\var{set(product(list(set5-set4),list(set4 and set5)))}$.</p>\n<p>Finalmente, $[(C \\cap D) \\times (C - D)] \\cup [(D - C) \\times (C \\cap D)]$ es el conjunto de todos los pares presentes en cualquiera de los conjuntos anteriores, i.e. $\\var{set16}$.</p>", "rulesets": {}, "extensions": [], "variables": {"list_extra": {"name": "list_extra", "group": "Lists", "definition": "[random(21..24)]", "description": "", "templateType": "anything"}, "set14": {"name": "set14", "group": "Ungrouped variables", 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