{"id":27422,"date":"2021-01-28T13:00:14","date_gmt":"2021-01-28T13:00:14","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27422"},"modified":"2024-07-09T02:29:12","modified_gmt":"2024-07-09T02:29:12","slug":"5-simetrias-da-logica-proposicional","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/","title":{"rendered":"5 Simetrias da L\u00f3gica Proposicional"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>5 Simetrias da L\u00f3gica Proposicional<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><em><strong>Resumo:<\/strong><br \/>Ao longo desta aula, exploraremos como a dupla nega\u00e7\u00e3o, o silogismo hipot\u00e9tico, o contrarrec\u00edproco da implica\u00e7\u00e3o, os teoremas de dedu\u00e7\u00e3o e as defini\u00e7\u00f5es dos conectivos se combinam para formar as simetrias da l\u00f3gica proposicional. Com demonstra\u00e7\u00f5es claras e simples, voc\u00ea aprender\u00e1 a dominar as equival\u00eancias e aplic\u00e1-las aos seus pr\u00f3prios desafios l\u00f3gicos.<\/p>\n<p>As simetrias abordadas na aula incluem: <span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span>-Simetria, <span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span>-Simetria, <span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span>-Simetria, <span class=\"katex-eq\" data-katex-display=\"false\">\\leftrightarrow<\/span>-Simetria e <span class=\"katex-eq\" data-katex-display=\"false\">\\veebar<\/span>-Simetria. Al\u00e9m disso, s\u00e3o destacadas as intera\u00e7\u00f5es entre as demonstra\u00e7\u00f5es, mostrando como cada uma apoia as anteriores para simplificar dedu\u00e7\u00f5es futuras. Esta aula n\u00e3o s\u00f3 fornecer\u00e1 um conhecimento profundo da L\u00f3gica Proposicional, mas tamb\u00e9m ensinar\u00e1 a usar demonstra\u00e7\u00f5es anteriores para otimizar seu processo de aprendizado.<br \/>\n<\/em><\/p>\n<p style=\"text-align:center;\"><strong><u>Objetivos de Aprendizagem<\/u>:<\/strong><br \/>At\u00e9 o final desta aula, o aluno ser\u00e1 capaz de<\/p>\n<ol>\n<li><strong>Recordar<\/strong> conceitos b\u00e1sicos da l\u00f3gica proposicional, como o silogismo hipot\u00e9tico e a dupla nega\u00e7\u00e3o.<\/li>\n<li><strong>Reconhecer<\/strong> as 5 Simetrias da L\u00f3gica Proposicional.<\/li>\n<li><strong>Compreender<\/strong> o processo de demonstra\u00e7\u00e3o das equival\u00eancias de simetrias.<\/li>\n<li><strong>Aplicar<\/strong> Presun\u00e7\u00e3o, Teorema de Dedu\u00e7\u00e3o e seu Rec\u00edproco nas demonstra\u00e7\u00f5es.<\/li>\n<li><strong>Relacionar<\/strong> as defini\u00e7\u00f5es de conectivos l\u00f3gicos com as simetrias.<\/li>\n<li><strong>Valorizar<\/strong> a import\u00e2ncia de realizar demonstra\u00e7\u00f5es apenas uma vez e reutiliz\u00e1-las em futuras demonstra\u00e7\u00f5es.<\/li>\n<li><strong>Desenvolver<\/strong> habilidades anal\u00edticas e cr\u00edticas ao realizar demonstra\u00e7\u00f5es l\u00f3gicas.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u00cdNDICE DE CONTE\u00daDOS<\/strong><br \/>\n<a href=\"#1\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span> &#8211; SIMETRIA<\/a><br \/>\n<a href=\"#2\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span> &#8211; SIMETRIA<\/a><br \/>\n<a href=\"#3\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span> &#8211; SIMETRIA<\/a><br \/>\n<a href=\"#4\"><span class=\"katex-eq\" data-katex-display=\"false\">\\leftrightarrow<\/span> &#8211; SIMETRIA<\/a><br \/>\n<a href=\"#5\"><span class=\"katex-eq\" data-katex-display=\"false\">\\veebar<\/span> &#8211; SIMETRIA<\/a><br \/>\n<a href=\"#6\">OBSERVA\u00c7\u00d5ES FINAIS<\/a>\n<\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/XKY_nS5Mizk\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">Uma consequ\u00eancia direta do silogismo hipot\u00e9tico, da dupla nega\u00e7\u00e3o e do contrarrec\u00edproco da implica\u00e7\u00e3o, dos teoremas de dedu\u00e7\u00e3o e das defini\u00e7\u00f5es dos conectivos s\u00e3o as 5 simetrias da l\u00f3gica proposicional que revisaremos a seguir.<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\downarrow \\beta) \\dashv\\vdash (\\beta\\downarrow \\alpha)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span><\/span>-Simetria<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\vee \\beta) \\dashv\\vdash (\\beta\\vee \\alpha)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-Simetria<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\wedge \\beta) \\dashv\\vdash (\\beta\\wedge \\alpha)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-Simetria<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\leftrightarrow \\beta) \\dashv\\vdash (\\beta\\leftrightarrow \\alpha)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\leftrightarrow<\/span><\/span>-Simetria<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\veebar \\beta) \\dashv\\vdash (\\beta\\veebar\\alpha)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\veebar<\/span><\/span>-Simetria<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">As demonstra\u00e7\u00f5es dessas equival\u00eancias n\u00e3o s\u00e3o totalmente triviais, mas, ao contr\u00e1rio de algumas demonstra\u00e7\u00f5es que j\u00e1 vimos, s\u00e3o bastante simples. Abaixo est\u00e1 a demonstra\u00e7\u00e3o de cada uma em uma dire\u00e7\u00e3o; a demonstra\u00e7\u00e3o na dire\u00e7\u00e3o inversa \u00e9 quase id\u00eantica e fica como exerc\u00edcio para o leitor.<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-Simetria<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=XKY_nS5Mizk&#038;t=203s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">assistir<\/span><\/strong><\/a><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta)\\}\\vdash (\\alpha \\vee\\beta)<\/span><\/span><\/td>\n<td>; Pre<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta)\\}\\vdash (\\neg \\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<td>; porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\vee \\beta) := (\\neg \\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta)\\}\\vdash (\\neg \\beta \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; CPI(2)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\vee \\beta)\\}\\vdash ( \\beta \\vee \\alpha)}<\/span><\/span><\/td>\n<td>; porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">( \\beta \\vee \\alpha) := (\\neg\\beta\\rightarrow\\alpha)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">O racioc\u00ednio na dire\u00e7\u00e3o inversa \u00e9 obtido com muito poucas varia\u00e7\u00f5es, come\u00e7ando com a presun\u00e7\u00e3o <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\beta\\vee\\alpha)\\}\\vdash (\\beta\\vee\\alpha)<\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span><\/span>-Simetria<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=XKY_nS5Mizk&#038;t=383s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">assistir<\/span><\/strong><\/a><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg(\\alpha \\downarrow \\beta)\\}\\vdash \\neg(\\alpha \\downarrow \\beta) <\/span><\/span><\/td>\n<td>; Pre<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg(\\alpha \\downarrow \\beta)\\}\\vdash (\\alpha \\vee \\beta) <\/span><\/span><\/td>\n<td>; de (1) porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> (\\alpha\\vee\\beta) := \\neg(\\alpha \\downarrow \\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg(\\alpha \\downarrow \\beta)\\}\\vdash (\\beta \\vee \\alpha) <\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-Simetria<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg(\\alpha \\downarrow \\beta) \\rightarrow (\\beta \\vee \\alpha)) <\/span><\/span><\/td>\n<td>; TD(3)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg(\\beta \\vee \\alpha) \\rightarrow (\\alpha \\downarrow \\beta)) <\/span><\/span><\/td>\n<td>; CPI(4)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ((\\beta \\downarrow \\alpha) \\rightarrow (\\alpha \\downarrow \\beta)) <\/span><\/span><\/td>\n<td>; de (5) porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\beta\\vee\\alpha) := \\neg(\\beta \\downarrow \\alpha)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(7)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\beta \\downarrow \\alpha) \\} \\vdash (\\alpha \\downarrow \\beta)}<\/span><\/span><\/td>\n<td>; RTD(6)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">Finalmente, raciocinando na dire\u00e7\u00e3o inversa, a dedu\u00e7\u00e3o \u00e9 obtida na dire\u00e7\u00e3o oposta come\u00e7ando com a presun\u00e7\u00e3o <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg(\\beta\\downarrow\\alpha)\\}\\vdash \\neg(\\beta\\downarrow\\alpha)<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-Simetria<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=XKY_nS5Mizk&#038;t=659s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">assistir<\/span><\/strong><\/a><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge \\beta)\\} \\vdash (\\alpha \\wedge \\beta)<\/span><\/span><\/td>\n<td>; Pre<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge \\beta)\\} \\vdash (\\neg\\alpha \\downarrow \\neg\\beta)<\/span><\/span><\/td>\n<td>; de (1) porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\wedge \\beta) := (\\neg\\alpha \\downarrow \\neg\\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge \\beta)\\} \\vdash (\\neg\\beta \\downarrow \\neg\\alpha)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span><\/span>-Simetria (2)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\wedge \\beta)\\} \\vdash ( \\beta \\wedge \\alpha)}<\/span><\/span><\/td>\n<td>; de (3) porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\beta \\wedge \\alpha) := (\\neg\\beta \\downarrow \\neg\\alpha)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">Assim como antes, se voc\u00ea raciocinar na dire\u00e7\u00e3o inversa, \u00e9 obtido com muito poucas varia\u00e7\u00f5es, come\u00e7ando com a presun\u00e7\u00e3o <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{( \\beta \\wedge \\alpha)\\}\\vdash ( \\beta \\wedge \\alpha)<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\leftrightarrow<\/span><\/span>-Simetria<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=XKY_nS5Mizk&#038;t=830s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">assistir<\/span><\/strong><\/a><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\leftrightarrow \\beta)\\} \\vdash (\\alpha \\leftrightarrow \\beta)<\/span><\/span><\/td>\n<td>; Pre<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\leftrightarrow \\beta)\\} \\vdash ((\\alpha \\rightarrow \\beta) \\wedge (\\alpha \\rightarrow \\beta))<\/span><\/span><\/td>\n<td>; De (1) porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\leftrightarrow \\beta) := ((\\alpha \\rightarrow \\beta) \\wedge (\\beta \\rightarrow \\alpha)) <\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\leftrightarrow \\beta)\\} \\vdash ((\\beta \\rightarrow \\alpha) \\wedge (\\alpha \\rightarrow \\beta) )<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-Simetria(2)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\leftrightarrow \\beta)\\} \\vdash (\\beta \\leftrightarrow \\alpha)}<\/span><\/span><\/td>\n<td>; De (3) porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\beta \\leftrightarrow \\alpha) := ((\\beta \\rightarrow \\alpha) \\wedge (\\alpha \\rightarrow \\beta)) <\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">Assim como o anterior, mas come\u00e7ando com a presun\u00e7\u00e3o <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{( \\beta \\leftrightarrow \\alpha)\\}\\vdash ( \\beta\\leftrightarrow \\alpha)<\/span><\/span><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\veebar<\/span><\/span>-Simetria<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=XKY_nS5Mizk&#038;t=982s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">assistir<\/span><\/strong><\/a><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\leftrightarrow \\beta)\\} \\vdash (\\alpha \\leftrightarrow \\beta) <\/span><\/span><\/td>\n<td>; Pre<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\leftrightarrow \\beta)\\} \\vdash ( \\beta \\leftrightarrow \\alpha) <\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\leftrightarrow<\/span><\/span>-Simetria(1)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ((\\alpha \\leftrightarrow \\beta) \\rightarrow ( \\beta \\leftrightarrow \\alpha)) <\/span><\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg ( \\beta \\leftrightarrow \\alpha) \\rightarrow \\neg (\\alpha \\leftrightarrow \\beta)) <\/span><\/span><\/td>\n<td>; CPI(3)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg ( \\beta \\leftrightarrow \\alpha)\\} \\vdash \\neg (\\alpha \\leftrightarrow \\beta) <\/span><\/span><\/td>\n<td>; RTD(4)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{ ( \\beta \\veebar \\alpha)\\} \\vdash (\\alpha \\veebar \\beta)} <\/span><\/span><\/td>\n<td>; De (5) porque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">( \\beta \\veebar \\alpha) := \\neg\\beta \\leftrightarrow \\alpha)<\/span><\/span> e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\veebar \\beta) := \\neg (\\alpha \\leftrightarrow \\beta)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">Como em todos os outros casos, basta testar a presun\u00e7\u00e3o na dire\u00e7\u00e3o inversa <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\beta \\leftrightarrow \\alpha)\\} \\vdash (\\beta \\leftrightarrow \\alpha)<\/span><\/span> para obter a dedu\u00e7\u00e3o nessa dire\u00e7\u00e3o.<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>Observa\u00e7\u00f5es Finais<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=XKY_nS5Mizk&#038;t=1145s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Um aspecto ao qual o leitor deve prestar aten\u00e7\u00e3o<\/span><\/strong><\/a> \u00e9 a ordem em que essas 5 simetrias da l\u00f3gica proposicional foram escolhidas para serem demonstradas. Note que cada uma \u00e9 feita de tal forma que usa algumas das demonstra\u00e7\u00f5es previamente realizadas. Isso reflete a abordagem que deve ser seguida ao realizar demonstra\u00e7\u00f5es: elas s\u00e3o feitas apenas uma vez (e nunca mais!); depois disso, seu objetivo deve ser usar as demonstra\u00e7\u00f5es anteriores para simplificar as futuras.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>5 Simetrias da L\u00f3gica Proposicional Resumo:Ao longo desta aula, exploraremos como a dupla nega\u00e7\u00e3o, o silogismo hipot\u00e9tico, o contrarrec\u00edproco da implica\u00e7\u00e3o, os teoremas de dedu\u00e7\u00e3o e as defini\u00e7\u00f5es dos conectivos se combinam para formar as simetrias da l\u00f3gica proposicional. Com demonstra\u00e7\u00f5es claras e simples, voc\u00ea aprender\u00e1 a dominar as equival\u00eancias e aplic\u00e1-las aos seus pr\u00f3prios [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27410,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":8,"footnotes":""},"categories":[607,621,571],"tags":[],"class_list":["post-27422","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-logica-matematica-pt","category-logica-proposicional-pt","category-matematica-pt"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>5 Simetrias da L\u00f3gica Proposicional - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"5 Simetrias da L\u00f3gica Proposicional\" \/>\n<meta property=\"og:description\" content=\"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-01-28T13:00:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-07-09T02:29:12+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"5 Simetrias da L\u00f3gica Proposicional\" \/>\n<meta name=\"twitter:description\" content=\"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"5 Simetrias da L\u00f3gica Proposicional\",\"datePublished\":\"2021-01-28T13:00:14+00:00\",\"dateModified\":\"2024-07-09T02:29:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/\"},\"wordCount\":1161,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/5simetrias.jpg\",\"articleSection\":[\"L\u00f3gica Matem\u00e1tica\",\"L\u00f3gica Proposicional\",\"Matem\u00e1tica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/\",\"name\":\"5 Simetrias da L\u00f3gica Proposicional - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#primaryimage\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/5simetrias.jpg\",\"datePublished\":\"2021-01-28T13:00:14+00:00\",\"dateModified\":\"2024-07-09T02:29:12+00:00\",\"description\":\"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#primaryimage\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/5simetrias.jpg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/5simetrias.jpg\",\"width\":1024,\"height\":356,\"caption\":\"Created with GIMP\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/pt\\\/5-simetrias-da-logica-proposicional\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"5 Simetrias da L\u00f3gica Proposicional\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"5 Simetrias da L\u00f3gica Proposicional - toposuranos.com\/material","description":"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/","og_locale":"es_ES","og_type":"article","og_title":"5 Simetrias da L\u00f3gica Proposicional","og_description":"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.","og_url":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-01-28T13:00:14+00:00","article_modified_time":"2024-07-09T02:29:12+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"5 Simetrias da L\u00f3gica Proposicional","twitter_description":"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"5 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"5 Simetrias da L\u00f3gica Proposicional","datePublished":"2021-01-28T13:00:14+00:00","dateModified":"2024-07-09T02:29:12+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/"},"wordCount":1161,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg","articleSection":["L\u00f3gica Matem\u00e1tica","L\u00f3gica Proposicional","Matem\u00e1tica"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/","url":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/","name":"5 Simetrias da L\u00f3gica Proposicional - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg","datePublished":"2021-01-28T13:00:14+00:00","dateModified":"2024-07-09T02:29:12+00:00","description":"Descubra as 5 Simetrias da L\u00f3gica Proposicional com demonstra\u00e7\u00f5es claras: dupla nega\u00e7\u00e3o, silogismo hipot\u00e9tico e mais.","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/5simetrias.jpg","width":1024,"height":356,"caption":"Created with GIMP"},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/pt\/5-simetrias-da-logica-proposicional\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"5 Simetrias da L\u00f3gica Proposicional"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27422","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=27422"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27422\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/27410"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=27422"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=27422"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=27422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}