{"id":388316,"date":"2019-06-16T01:41:26","date_gmt":"2019-06-16T04:41:26","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=388316"},"modified":"2019-06-16T03:44:13","modified_gmt":"2019-06-16T06:44:13","slug":"questao-comentada-02-ita","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/questao-comentada-02-ita\/","title":{"rendered":"Quest\u00e3o resolvida 02 (ITA)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Ol\u00e1, guerreiros e guerreiras!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Neste artigo comentarei uma quest\u00e3o de <strong>CONJUNTOS<\/strong> que foi cobrada no concurso do <strong>Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA)<\/strong>, em <strong>2000<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"text-align:center\"><strong>QUEST\u00c3O<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(ITA &#8211; 2000) <\/strong>Denotaremos por n(x) o n\u00famero de elementos de um conjunto finito x. Sejam A, B, C conjuntos tais que n(AUB) = 8,\u00a0\u00a0 n(AUC) = 9 \u00a0\u00a0e \u00a0    n(BUC) = 10,\u00a0 \u00a0n(AUBUC) = 11\u00a0\u00a0e\u00a0\u00a0n(A\u22c2B\u22c2C) = 2. Ent\u00e3o, n(A) + n(B) + n(C) \u00e9 igual a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) 11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) 14<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) 15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) 18<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e) 25<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"text-align:center\"><strong>RESOLU\u00c7\u00c3O<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A quest\u00e3o\nforneceu os seguintes dados:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; n(AUB)\n= 8;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; n(AUC)\n= 9;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; n(BUC)\n= 10;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211;\nn(AUBUC) = 11;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; n(A\u22c2B\u22c2C) = 2;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; n(A) +\nn(B) + n(C) = ?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Resolveremos a quest\u00e3o atrav\u00e9s das f\u00f3rmulas de conjuntos:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I) n(AUB) = n(A) + n(B) \u2013 n(A\u22c2B)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 8 = n(A) + n(B) \u2013 n(A\u22c2B)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 <strong>n(A\u22c2B) = n(A) + n(B) \u2013 8<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">II)\nn(AUC) = n(A) + n(C) \u2013 n(A\u22c2C)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 9 = n(A) + n(C) \u2013 n(A\u22c2C)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 <strong>n(A\u22c2C) = n(A) + n(C) \u2013 9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">III)\nn(BUC) = n(B) + n(C) \u2013 n(B\u22c2C)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 10 = n(B) + n(C) \u2013 n(B\u22c2C)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 <strong>n(B\u22c2C) = n(B) + n(C) \u2013 10<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vamos\nsubstituir (I), (II) e (III) em (IV):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IV)\nn(AUBUC) = n(A) + n(B) + n(C) \u2013 n(A\u22c2B) \u2013 n(A\u22c2C) \u2013 n(B\u22c2C) + n(A\u22c2B\u22c2C)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 n(AUBUC) = n(A) + n(B) + n(C) \u2013 n(A\u22c2B) \u2013 n(A\u22c2C) \u2013\nn(B\u22c2C) + n(A\u22c2B\u22c2C)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 11 = n(A) + n(B) + n(C) \u2013 [n(A) + n(B) \u2013 8]\n\u2013 [n(A) + n(C) \u2013 9] \u2013 [n(B)\n+ n(C) \u2013 10] + 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 11 = n(A) + n(B) + n(C) \u2013 n(A) \u2013 n(B) + 8 \u2013 n(A) \u2013 n(C) + 9 \u2013 n(B) \u2013\nn(C) + 10 + 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 11 = \u2013 n(A) + 8 \u2013 n(C) + 9 \u2013 n(B) + 10 + 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 n(A) + n(B) + n(C) = 8 + 9 + 10 + 2 \u2013 11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27f9 n(A) + n(B) + n(C) = 18<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>GABARITO: D<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aqui termina o nosso artigo.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Um abra\u00e7o!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Fiquem com DEUS e bons estudos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Carlos Vitor<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ol\u00e1, guerreiros e guerreiras! Neste artigo comentarei uma quest\u00e3o de CONJUNTOS que foi cobrada no concurso do Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), em 2000. QUEST\u00c3O (ITA &#8211; 2000) Denotaremos por n(x) o n\u00famero de elementos de um conjunto finito x. Sejam A, B, C conjuntos tais que n(AUB) = 8,\u00a0\u00a0 n(AUC) = 9 \u00a0\u00a0e \u00a0 [&hellip;]<\/p>\n","protected":false},"author":1224,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[1],"tags":[],"tax_estado":[],"class_list":["post-388316","post","type-post","status-publish","format-standard","hentry","category-cursos-e-concursos"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.7 (Yoast SEO v27.7) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Quest\u00e3o resolvida 02 (ITA)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blog-estrategia.mystagingwebsite.com\/questao-comentada-02-ita\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quest\u00e3o resolvida 02 (ITA)\" \/>\n<meta property=\"og:description\" content=\"Ol\u00e1, guerreiros e guerreiras! Neste artigo comentarei uma quest\u00e3o de CONJUNTOS que foi cobrada no concurso do Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), em 2000. QUEST\u00c3O (ITA &#8211; 2000) Denotaremos por n(x) o n\u00famero de elementos de um conjunto finito x. Sejam A, B, C conjuntos tais que n(AUB) = 8,\u00a0\u00a0 n(AUC) = 9 \u00a0\u00a0e \u00a0 [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blog-estrategia.mystagingwebsite.com\/questao-comentada-02-ita\/\" \/>\n<meta property=\"og:site_name\" content=\"Estrat\u00e9gia Concursos\" \/>\n<meta property=\"article:published_time\" content=\"2019-06-16T04:41:26+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-16T06:44:13+00:00\" \/>\n<meta name=\"author\" content=\"Carlos Vitor\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@EstratConcursos\" \/>\n<meta name=\"twitter:site\" content=\"@EstratConcursos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Carlos Vitor\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" 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