{"id":1701177,"date":"2026-01-29T14:44:00","date_gmt":"2026-01-29T17:44:00","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=1701177"},"modified":"2026-01-28T10:13:28","modified_gmt":"2026-01-28T13:13:28","slug":"diagramas-venn","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/diagramas-venn\/","title":{"rendered":"Diagramas de Venn"},"content":{"rendered":"\n<p>Ol\u00e1, pessoal! Como est\u00e3o? Hoje, iremos tratar sobre os Diagramas de Venn. Esse tema, muitas vezes, n\u00e3o aparece <a href=\"https:\/\/docs.uberlandia.mg.gov.br\/wp-content\/uploads\/2022\/09\/Edital-Concurso-assinado.pdf\">expresso no edital<\/a>, por\u00e9m, usamos em diversas quest\u00f5es tanto de racioc\u00ednio l\u00f3gico quanto de matem\u00e1tica em si. \u00c9 um assunto b\u00e1sico, mas muito importante.<\/p>\n\n\n<figure class=\"wp-block-post-featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1969\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-scaled.jpg\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"Diagramas de Venn\" style=\"object-fit:cover;\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-scaled.jpg 2560w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-300x231.jpg 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-1024x788.jpg 1024w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-768x591.jpg 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-1536x1182.jpg 1536w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-2048x1575.jpg 2048w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2025\/08\/13115036\/24644996_tiny-students-with-huge-sign-pi-flat-vector-illustration-150x115.jpg 150w\" sizes=\"auto, (max-width: 2560px) 100vw, 2560px\" \/><\/figure>\n\n\n<h2 class=\"wp-block-heading\" id=\"h-conceito-dos-diagramas-de-venn\">Conceito dos Diagramas de Venn<\/h2>\n\n\n\n<p>Incialmente, esse nome &#8220;<strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#cf2e2e\" class=\"has-inline-color\">Venn<\/mark><\/strong>&#8221; se trata de homenagem ao matem\u00e1tico e fil\u00f3sofo brit\u00e2nico\u00a0<strong>John Venn<\/strong>, que popularizou o m\u00e9todo no s\u00e9culo XIX para representar graficamente as rela\u00e7\u00f5es l\u00f3gicas entre conjuntos.<\/p>\n\n\n\n<p>Nobres, um &#8220;conjunto&#8221; \u00e9 a reuni\u00e3o de itens semelhantes, ou sejam que apresentam alguma particularidade em comum. Na matem\u00e1tica, <em>simbologicamente<\/em>, usamos chaves {  } para represent\u00e1-los.<\/p>\n\n\n\n<p>Os Diagramas de Veen, nesse toada, trazem-nos uma apresenta\u00e7\u00e3o mais visual das rela\u00e7\u00f5es entre os conjuntos, de forma que sa\u00edmos dessa &#8220;confus\u00e3o&#8221; de letras e representa\u00e7\u00f5es matem\u00e1ticas e vamos para algo mais visual, que facilita nossa aprendizagem.<\/p>\n\n\n\n<p>Assim, vamos supor que voc\u00ea est\u00e1 em sua sala de aula e separe seus colegas em dois grupos: quem pratica atletismo(A), quem joga basquete(B) e quem pratica ambos os esportes(atletismo e basquete).<\/p>\n\n\n\n<p>Matematicamente, representar\u00edamos essa express\u00e3o da seguinte forma:<\/p>\n\n\n\n<figure class=\"wp-block-pullquote\"><blockquote><p>(<em>A U B<\/em>) = (A) + (<em>B<\/em>) &#8211; (A \u2229\u00a0<em>B<\/em>).<\/p><cite><em>U significa Uni\u00e3o e \u2229 significa interse\u00e7\u00e3o<\/em><\/cite><\/blockquote><\/figure>\n\n\n\n<p>Em que:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(<em>A U B<\/em>) \u00e9 quem pratica algum dos esportes ou ambos;<\/li>\n\n\n\n<li>(A) \u00e9 quem pratica atletismo;<\/li>\n\n\n\n<li>(B) \u00e9 quem pratica basquete;<\/li>\n\n\n\n<li>(A \u2229\u00a0<em>B<\/em>) \u00e9 quem pratica ambos os esporte.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-aplicacao-dos-diagramas-de-venn\">Aplica\u00e7\u00e3o dos Diagramas de Venn<\/h2>\n\n\n\n<p>Vamos usar os Diagramas de Venn para representar nosso exemplo da sala de aula.<\/p>\n\n\n\n<p>Vamos supor que 80(oitenta) pratiquem s\u00f3 atletismo; 100(cem) s\u00f3 basquete, 20(vinte) pratique ambos os esportes e 10(dez) n\u00e3o pratique nenhum dos esportes. Como ficaria o Diagrama de Venn?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"414\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21002312\/image-226.png\" alt=\"Diagramas de Venn com 2 conjuntos\" class=\"wp-image-1702669\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21002312\/image-226.png 700w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21002312\/image-226-300x177.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21002312\/image-226-150x89.png 150w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure>\n\n\n\n<p>Entretanto, nobres, observem uma coisa: H\u00e1 20(vinte) alunos que participam dos dois grupos e, assim, se ped\u00edssemos quantos alunos praticam algum esporte, o resultado n\u00e3o poderia ser alcan\u00e7ado somando 80+<em>20<\/em>+100+<em>20<\/em> = <strong><em>220<\/em><\/strong>, pois estar\u00edamos &#8220;contando&#8221; o 20(vinte) duas vezes. <\/p>\n\n\n\n<p>Voltemos \u00e0 formula para entender:<\/p>\n\n\n\n<p>(<em>A U B<\/em>) = (A) + (<em>B<\/em>) &#8211; (A \u2229\u00a0<em>B<\/em>)<\/p>\n\n\n\n<p>(<em>A U B<\/em>) = [80 + 20] + [100 + 20] &#8211; 20<\/p>\n\n\n\n<p>Logo, (<em>A U B<\/em>) = <strong>200<\/strong><\/p>\n\n\n\n<p>Ou seja, o n\u00ba de alunos que pratica &#8220;algum&#8221; esporte \u00e9 200(duzentos).<\/p>\n\n\n\n<p>Logo, amigo(as), \u00e9 isso que o diagrama faz, ele sistematiza, de maneira visual, a rela\u00e7\u00e3o e os valores entre os grupos.<\/p>\n\n\n\n<p>Ent\u00e3o, nas quest\u00f5es, fiquem atentos. Se a banca citar: &#8220;100 alunos praticam atletismo&#8221;. Nesse valor est\u00e1 embutido tanto que pratica <strong>s\u00f3 <\/strong>atletismo, quanto quem pratica atletismo e outro esporte.<\/p>\n\n\n\n<p>Apesar de o Diagrama de <em>Venn <\/em>com dois conjuntos ser bem conhecido, o que possui 3(tr\u00eas) conjuntos \u00e9 o que mais cai em prova.<\/p>\n\n\n\n<p>Vejamos a imagem:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"740\" height=\"522\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21003753\/image-227.png\" alt=\"Diagramas de Venn com 3 conjuntos\" class=\"wp-image-1702671\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21003753\/image-227.png 740w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21003753\/image-227-300x212.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21003753\/image-227-150x106.png 150w\" sizes=\"auto, (max-width: 740px) 100vw, 740px\" \/><\/figure>\n\n\n\n<p>Observem que a l\u00f3gica \u00e9 a mesma (a, b e c) e suas interse\u00e7\u00f5es.<\/p>\n\n\n\n<p>A f\u00f3rmula matem\u00e1tica \u00e9:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>n(A\u222aB\u222aC)=n(A)+n(B)+n(C)\u2212n(A\u2229B)\u2212n(A\u2229C)\u2212n(B\u2229C)+n(A\u2229B\u2229C)<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-exemplo-dos-diagramas-de-venn-pratica\">Exemplo dos Diagramas de Venn pr\u00e1tica<\/h2>\n\n\n\n<p>Vamos usar uma quest\u00e3o recent\u00edssima cobrada no concurso da Guarda Civil Municipal de Paulista (PE) aplicada pela IGEDUC.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p id=\"03762224Q-324588da-2d6b576a02f7\">Foi realizado um levantamento em uma turma de 60 alunos, sobre a frequ\u00eancias dos alunos em tr\u00eas disciplinas optativas: Matem\u00e1tica, F\u00edsica e Qu\u00edmica. Os resultados foram:<\/p>\n\n\n\n<p id=\"03762224Q-cea0d44a-9a4c7e8ea0aa\">30 alunos frequentam as aulas de Matem\u00e1tica;<\/p>\n\n\n\n<p id=\"03762224Q-27aa1850-eb2703f5d872\">25 frequentam as aulas de F\u00edsica;<\/p>\n\n\n\n<p id=\"03762224Q-addddee5-93194c58993d\">20 frequentam as aulas de Qu\u00edmica;<\/p>\n\n\n\n<p id=\"03762224Q-e901ef4e-dca88ea8402e\">12 frequentam as aulas de Matem\u00e1tica e F\u00edsica;<\/p>\n\n\n\n<p id=\"03762224Q-ab47cd36-c273ce54e401\">8 frequentam as aulas de Matem\u00e1tica e Qu\u00edmica;<\/p>\n\n\n\n<p id=\"03762224Q-73dd5510-7ef4b0247880\">6 frequentam as aulas de F\u00edsica e Qu\u00edmica;<\/p>\n\n\n\n<p id=\"03762224Q-30473711-f60df65cff88\">4 frequentam as aulas das tr\u00eas disciplinas.<\/p>\n\n\n\n<p id=\"03762224Q-87f3ede5-bbf18913bef9\">Com base nestas informa\u00e7\u00f5es, assinale a alternativa que apresenta corretamente <strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#cf2e2e\" class=\"has-inline-color\">quantos alunos n\u00e3o frequentam nenhuma das tr\u00eas disciplinas<\/mark><\/strong>?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(A)\u00a07 alunos.<\/li>\n\n\n\n<li>(B) 5 alunos.<\/li>\n\n\n\n<li>(C) 9 alunos.<\/li>\n\n\n\n<li>(D) 11 alunos.<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<p><strong>Coment\u00e1rios<\/strong>: Vamos montar o diagrama tal qual aprendemos &#8211; <em>Obs. Na prova, pessoal, sugerimos que desenhem mesmo, ok?!<\/em><\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#9b51e0\" class=\"has-inline-color\">Dica 1<\/mark><\/strong>: Nos Diagramas de Venn, sempre comecem pela interse\u00e7\u00e3o dos 3(tr\u00eas) conjuntos(<em>interse\u00e7\u00e3o central<\/em>). Nesse caso, 4 alunos frequentam as 3(tr\u00eas) disciplinas. <\/p>\n\n\n\n<p>Ap\u00f3s, <strong>de todas as demais interse\u00e7\u00f5es<\/strong>, diminuam o valor correspondente \u00e0s 3(tr\u00eas) interse\u00e7\u00f5es a fim de n\u00e3o incorrer em dupla contagem. Vamos ver como fica nosso diagrama apenas com esses dados:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"747\" height=\"507\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21005027\/image-228.png\" alt=\"\" class=\"wp-image-1702677\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21005027\/image-228.png 747w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21005027\/image-228-300x204.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21005027\/image-228-150x102.png 150w\" sizes=\"auto, (max-width: 747px) 100vw, 747px\" \/><\/figure>\n\n\n\n<p>Visualizem que o valor das 3(tr\u00eas) interse\u00e7\u00f5es &#8211; valor central do gr\u00e1fico &#8211; se manteve. J\u00e1 das demais interse\u00e7\u00f5es, precisamos subtrair o valor da interse\u00e7\u00e3o central. Ficou assim:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>M\u2229F = 12(dado na quest\u00e3o) &#8211; 4(quem faz as 3 mat\u00e9rias) = 8<\/li>\n\n\n\n<li>M\u2229Q = 8(dado na quest\u00e3o) &#8211; 4(quem faz as 3 mat\u00e9rias) = 5<\/li>\n\n\n\n<li>F\u2229Q = 6(dado na quest\u00e3o) &#8211; 4(quem faz as 3 mat\u00e9rias) = 2<\/li>\n<\/ul>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#9b51e0\" class=\"has-inline-color\">Dica 2<\/mark><\/strong>. S\u00f3 ap\u00f3s achar as interse\u00e7\u00f5es, encontre quem pertence &#8220;exclusivamente&#8221; a um s\u00f3 conjunto. <\/p>\n\n\n\n<p>Vamos mat\u00e9ria por mat\u00e9ria:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>F\u00edsica: 25(dado na quest\u00e3o) <strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#0693e3\" class=\"has-inline-color\"> &#8211; 8 &#8211; 4 &#8211; 2.<\/mark><\/strong> Logo F = 11;<\/li>\n\n\n\n<li>Matem\u00e1tica: 30(dado na quest\u00e3o) <strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#0693e3\" class=\"has-inline-color\">&#8211; 8 &#8211; 4 &#8211; 4<\/mark><\/strong>. logo M = 14;<\/li>\n\n\n\n<li>Qu\u00edmica: 20(dado na quest\u00e3o) <strong><mark style=\"background-color:rgba(0, 0, 0, 0);color:#0693e3\" class=\"has-inline-color\">&#8211; 4 &#8211; 4 &#8211; 2<\/mark><\/strong>. Logo Q = 10<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"751\" height=\"525\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21010527\/image-229.png\" alt=\"\" class=\"wp-image-1702679\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21010527\/image-229.png 751w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21010527\/image-229-300x210.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/01\/21010527\/image-229-150x105.png 150w\" sizes=\"auto, (max-width: 751px) 100vw, 751px\" \/><\/figure>\n\n\n\n<p>A quest\u00e3o solicita quantos dos 60(sessenta) alunos n\u00e3o frequentam nenhuma das 3 mat\u00e9rias.<\/p>\n\n\n\n<p>A\u00ed, \u00e9 s\u00f3 somar todos os valores do Diagrama: 14 + 11 + 10 + 8 + 4 + 4 + 2 = 53.<\/p>\n\n\n\n<p>Dessa forma, 60 &#8211; 53 = 7 alunos n\u00e3o frequentam nenhuma das mat\u00e9rias. <strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-accent-3-color\">Gab. A<\/mark><\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-conclusao\">Conclus\u00e3o<\/h2>\n\n\n\n<p>Nobres, \u00e9 isso que t\u00ednhamos para falar sobre os Diagramas de Venn. \u00c9 uma ferramenta muito \u00fatil quando estamos diante de quest\u00f5es quem envolvem conjuntos. Refor\u00e7amos mais uma vez aten\u00e7\u00e3o na leitura da quest\u00e3o para a correta interpreta\u00e7\u00e3o e inser\u00e7\u00e3o dos valores do diagrama. E, na hora da prova, tentem desenhar para evitar &#8220;perder&#8221; uma quest\u00e3o por &#8220;Bobeira&#8221;.<\/p>\n\n\n\n<p>Abra\u00e7os e bons estudos!<\/p>\n\n\n\n<p class=\"has-text-align-left\"><em>Quer estar antenado aos pr\u00f3ximos concursos previstos? Confira nossos artigos!<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-vivid-cyan-blue-background-color has-text-color has-background has-link-color wp-elements-9603f785c0eec09bc6030dcf96ae9ff9\"><a href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/concursos-abertos\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-black-color\">Concursos Abertos<\/mark><\/strong><\/a><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-vivid-cyan-blue-background-color has-text-color has-background has-link-color wp-elements-035e8bba74ba04b5f8015d417e24c8dd\"><a href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/concursos-2026\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-black-color\">Concursos 2026<\/mark><\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ol\u00e1, pessoal! Como est\u00e3o? Hoje, iremos tratar sobre os Diagramas de Venn. Esse tema, muitas vezes, n\u00e3o aparece expresso no edital, por\u00e9m, usamos em diversas quest\u00f5es tanto de racioc\u00ednio l\u00f3gico quanto de matem\u00e1tica em si. \u00c9 um assunto b\u00e1sico, mas muito importante. Conceito dos Diagramas de Venn Incialmente, esse nome &#8220;Venn&#8221; se trata de homenagem [&hellip;]<\/p>\n","protected":false},"author":2891,"featured_media":1622782,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[1],"tags":[],"tax_estado":[],"class_list":["post-1701177","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cursos-e-concursos"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.2 (Yoast SEO v27.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Diagramas de Venn<\/title>\n<meta name=\"description\" content=\"Trataremos sobre os Diagramas de Venn, abordando sua f\u00f3rmula matem\u00e1tica, import\u00e2ncia e aplica\u00e7\u00e3o em quest\u00f5es de concursos.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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