{"id":33853,"date":"2021-02-14T15:00:05","date_gmt":"2021-02-14T15:00:05","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33853"},"modified":"2025-07-31T23:23:06","modified_gmt":"2025-07-31T23:23:06","slug":"leges-demorgan-distributionis-earumque-demonstrationes","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/","title":{"rendered":"Leges DeMorgan, Distributionis earumque Demonstrationes"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Leges DeMorgan, Distributionis earumque Demonstrationes<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>SUMMARIUM<\/strong><br \/><em>In hac lectione tractantur demonstrationes legum DeMorgan et distributionis coniunctionis ac disiunctionis, quae frequenter in logica propositionali adhibentur necnon in disciplinis talibus quales sunt theoria congregationum, probabilitates, topologia, electronica et programmatio. Exponuntur aequivalentiae quae distributionem negationum cum coniunctione et disiunctione formaliter exprimunt, sicut etiam regulas distributivitatis inter coniunctionem et disiunctionem. Explicantur technicae deductionis adhibitae ad has demonstrationes obtinendas, atque discipulus incitatur ut demonstrationes propositas perficiat ad scientiam suam confirmandam. Suadetur quoque exercitatio qua quaestio proponatur: \u00abPossumne has demonstrationes alio ordine componere eadem methodologia utens?\u00bb ad artes logicas excolendas.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>PROPOSITA DISCENDI:<\/strong><br \/>\nPost hanc lectionem, discipulus poterit\n<\/p>\n<ol>\n<li><strong>Demonstr\u0101re<\/strong> leges DeMorgan et regulas distributivitatis inter coniunctionem et disiunctionem.<\/li>\n<li><strong>Applic\u0101re<\/strong> technicas deductionis ad demonstrationem legum DeMorgan et distributivitatis.<\/li>\n<li><strong>Compar\u0101re<\/strong> demonstrationes legum DeMorgan et distributivitatis ad similitudines atque differentias explorandas.<\/li>\n<li><strong>Analys\u0101re<\/strong> demonstrationes legum DeMorgan et distributivitatis ad intellegentiam logicae propositionis augendam.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX<\/strong><br \/>\n<a href=\"#1\">LEGES DEMORGAN<\/a><br \/>\n<a href=\"#2\">REGULAE DISTRIBUTIVITATIS INTER CONIUNCTIONEM ET DISIUNCTIONEM<\/a><br \/>\n<a href=\"#2\">CONSIDERATIONES FINALES<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ntfTrdqIipo\" 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;\">Nunc alia proprietas saepe in logica propositionali adhibita excutitur, scilicet demonstrationes legum DeMorgan de distributione coniunctionis et disiunctionis. Usus harum legum solitus est in theoria congregationum et, exinde, totam mathematicam permeant: a theoria probabilitatum ad topologiam, quin etiam praesentiam habent in electronica et programmatio. Consuetudine recepta, has demonstrationes evolvemus ex technicis deductionis quas hactenus didicimus.<\/p>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Leges DeMorgan<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=709s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Leges DeMorgan<\/span><\/strong><\/a> sunt coniunctio aequivalentiarum quae distributionem negationum cum coniunctione et disiunctione formaliter exprimunt. Formaliter exprimuntur per aequivalentias:<\/p>\n<p style=\"text-align: center; color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha \\wedge \\beta) \\dashv \\vdash (\\neg\\alpha \\vee \\neg \\beta)<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha \\vee \\beta) \\dashv \\vdash (\\neg\\alpha \\wedge \\neg \\beta)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Hae aequivalentiae probatae sine demonstratione stricta, qualem hactenus exhibuimus, elici possunt, quoniam definita coniunctionis et disiunctionis, una cum regula negationis duplicis et substitutionibus, satis sunt. Ex definitione coniunctionis sequitur:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(A \\wedge B):= \\neg(\\neg A \\vee \\neg B)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Negationem ad utrumque latus huius expressionis applicando, obtinemus<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(A \\wedge B):= \\neg\\neg(\\neg A \\vee \\neg B)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Deinde, per aequivalentiam negationis duplicis, habemus<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(A \\wedge B)\\dashv \\vdash (\\neg A \\vee \\neg B)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Postremo, ponendo <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=\\alpha<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B=\\beta<\/span><\/span>, obtinemus primam aequivalentiam DeMorgan<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\neg(\\alpha \\wedge \\beta) \\dashv \\vdash (\\neg\\alpha \\vee \\neg \\beta)}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Ad alteram obtinendam, iterum negationem ad utrumque latus expressionis prius consideratae applicamus, unde fit<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg\\neg(A \\wedge B)\\dashv \\vdash \\neg(\\neg A \\vee \\neg B)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Et per negationem duplicem sequitur<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\neg A \\vee \\neg B) \\dashv \\vdash (A \\wedge B)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Si in hac ultima aequivalentia ponimus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=\\neg\\alpha<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B=\\neg\\beta<\/span><\/span>, tunc habemus<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\neg \\neg\\alpha \\vee \\neg \\neg\\beta) \\dashv \\vdash (\\neg\\alpha \\wedge \\neg\\beta)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Quae, propter negationem duplicem, ad secundam aequivalentiam DeMorgan ducit<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\neg( \\alpha \\vee \\beta) \\dashv \\vdash (\\neg\\alpha \\wedge \\neg\\beta)}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Praeterea, simili ratione assequi possumus alias formas, quae nihil aliud sunt nisi variationes eorum quae recensuimus<\/p>\n<p style=\"text-align: center; color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\neg\\alpha \\wedge \\beta) \\dashv \\vdash (\\alpha \\vee \\neg \\beta)<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\neg\\alpha \\vee \\beta) \\dashv \\vdash (\\alpha \\wedge \\neg \\beta)<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha \\wedge \\neg\\beta) \\dashv \\vdash (\\neg\\alpha \\vee \\beta)<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha \\vee \\neg\\beta) \\dashv \\vdash (\\neg\\alpha \\wedge \\beta)<\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Regulae Distributivitatis inter Coniunctionem et Disiunctionem<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=709s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Ut nomen indicat<\/span><\/strong><\/a>, hae regulae nobis permittunt coniunctiones et disiunctiones intra expressionem distribuere. Hae leges in sequentibus duabus aequivalentibus comprehenduntur:<\/p>\n<table style=\"text-align: left;\">\n<tbody>\n<tr>\n<td>\u2227 &#8211; Distributivitas<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\wedge(\\beta \\vee \\gamma)) \\dashv \\vdash ((\\alpha \\wedge \\beta)\\vee(\\alpha \\wedge \\gamma)) <\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u2228 &#8211; Distributivitas<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\vee(\\beta \\wedge \\gamma)) \\dashv \\vdash ((\\alpha \\vee \\beta)\\wedge(\\alpha \\vee \\gamma)) <\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Ut iam fieri consuevit in his quae antea tractavimus, etsi haec est conclusio nota, eius demonstratio haudquaquam est trivialis. Quamquam ad hanc demonstrationem perficiendam ratiocinatio in utraque directione est necessaria, hoc loco solum demonstrationem unius directionis afferam; demonstratio in alteram directionem pro exercitio lectori relinquitur.<\/p>\n<h3>\u2227 &#8211; Distributivitas<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=831s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Ut demonstretur quod evenit<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma))\\}\\vdash((\\alpha \\wedge \\beta)\\vee(\\alpha \\wedge \\gamma))<\/span><\/span>, sequens ratio adhibetur.<\/p>\n<table style=\"text-align: left;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\beta \\}\\vdash (\\alpha \\wedge(\\beta \\vee\\gamma)) <\/span><\/span><\/td>\n<td>; Praemissa<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\beta \\}\\vdash \\alpha <\/span><\/span><\/td>\n<td>; \u2227-Eliminatio(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\beta \\}\\vdash \\beta <\/span><\/span><\/td>\n<td>; Praemissa<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\beta \\}\\vdash (\\alpha\\wedge \\beta) <\/span><\/span><\/td>\n<td>; \u2227-Introductio(2,3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\beta \\}\\vdash ((\\alpha\\wedge \\beta)\\vee(\\alpha \\wedge \\gamma) )<\/span><\/span><\/td>\n<td>; \u2228-Introductio(4)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\neg\\beta \\}\\vdash (\\alpha \\wedge(\\beta \\vee\\gamma)) <\/span><\/span><\/td>\n<td>; Praemissa<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\neg\\beta \\}\\vdash (\\beta \\vee\\gamma) <\/span><\/span><\/td>\n<td>; \u2227-Eliminatio(6)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\neg\\beta \\}\\vdash\\neg\\beta <\/span><\/span><\/td>\n<td>; Praemissa<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\neg\\beta \\}\\vdash\\gamma <\/span><\/span><\/td>\n<td>; \u2228-Eliminatio(7,8)<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\neg\\beta \\}\\vdash\\alpha <\/span><\/span><\/td>\n<td>; \u2227-Eliminatio(6)<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\neg\\beta \\}\\vdash (\\alpha\\wedge\\gamma) <\/span><\/span><\/td>\n<td>; \u2227-Introductio(9,10)<\/td>\n<\/tr>\n<tr>\n<td>(12)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma)), \\neg\\beta \\}\\vdash ((\\alpha\\wedge\\beta)\\vee(\\alpha\\wedge\\gamma)) <\/span><\/span><\/td>\n<td>; \u2228-Introductio(11)<\/td>\n<\/tr>\n<tr>\n<td>(13)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\wedge(\\beta \\vee\\gamma))\\}\\vdash ((\\alpha\\wedge\\beta)\\vee(\\alpha\\wedge\\gamma))} <\/span><\/span><\/td>\n<td>; Casus(5,12)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Hoc modo demonstratum est <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge(\\beta \\vee\\gamma))\\}\\vdash((\\alpha \\wedge \\beta)\\vee(\\alpha \\wedge \\gamma))<\/span><\/span>. Nunc tua est pars ut exercitia expleas: conare per te demonstrare quod <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{((\\alpha \\wedge \\beta)\\vee(\\alpha \\wedge \\gamma))\\}\\vdash (\\alpha \\wedge(\\beta \\vee\\gamma))<\/span><\/span>.<\/p>\n<h3>\u2228 &#8211; Distributivitas<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=1449s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Demonstratio<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma))\\}\\vdash((\\alpha \\vee \\beta)\\wedge(\\alpha \\vee \\gamma))<\/span><\/span> ex sequenti ratiocinatione elici potest:<\/p>\n<table style=\"text-align: left;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma)), \\neg\\alpha\\}\\vdash (\\alpha \\vee(\\beta \\wedge\\gamma))<\/span><\/span><\/td>\n<td>; Praemissa<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma)), \\neg\\alpha\\}\\vdash \\neg\\alpha<\/span><\/span><\/td>\n<td>; Praemissa<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma)), \\neg\\alpha\\}\\vdash (\\beta \\wedge\\gamma)<\/span><\/span><\/td>\n<td>; \u2228-Eliminatio(1,2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma)), \\neg\\alpha\\}\\vdash \\beta<\/span><\/span><\/td>\n<td>; \u2227-Eliminatio(3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma)), \\neg\\alpha\\}\\vdash \\gamma<\/span><\/span><\/td>\n<td>; \u2227-Eliminatio(3)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma))\\}\\vdash (\\neg\\alpha\\rightarrow \\beta)<\/span><\/span><\/td>\n<td>; Deductio Temporalis (4)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma))\\}\\vdash (\\alpha\\vee \\beta)<\/span><\/span><\/td>\n<td>; <span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span>-Definitio(6)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma))\\}\\vdash (\\neg\\alpha \\rightarrow \\gamma)<\/span><\/span><\/td>\n<td>; Deductio Temporalis (5)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee(\\beta \\wedge\\gamma))\\}\\vdash (\\alpha \\vee \\gamma)<\/span><\/span><\/td>\n<td>; <span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span>-Definitio(8)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\vee(\\beta \\wedge\\gamma))\\}\\vdash ((\\alpha\\vee \\beta) \\wedge (\\alpha \\vee \\gamma))}<\/span><\/span><\/td>\n<td>; \u2227-Introductio(7,9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Haec est pars prima demonstrationis; nunc sola pars inversa restat, sed illa tibi, lector, exercitium relinquetur :3<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Considerationes Finales<\/h2>\n<p style=\"text-align: justify;\">His recensionibus quas de demonstrationibus legum DeMorgan de distributione coniunctionis et disiunctionis fecimus, perficere possumus nostrum studium de technicis deductionis logicae propositionis et de modo quo hae technicae in demonstrationem legum logicae classicae, saltem earum potissimarum, conveniunt.<\/p>\n<p style=\"text-align: justify;\">Maximi momenti est omnes demonstrationes propositae complere, ut cognitio harum technicarum confirmetur. Ad difficultatem levandam, valde utile est demonstrationes inter se comparare ad similitudines detegendas, cum fieri possit ut eadem ratio quae in una demonstratione successit, mutatis quibusdam, etiam in alia utilis sit.<\/p>\n<p style=\"text-align: justify;\">Ultimum quod monendum est, ordo est quem ad has demonstrationes evolvendas elegi. Animadvertere debes quod unaquaeque demonstratio innitebatur aliquibus prioribus demonstrationibus. Hunc ordinem elegi quia mihi ipse facilius visus est. Exercitatio bona ad artes tuas in his rebus augendas est te ipsum interrogare: \u201cPossumne has demonstrationes alio ordine componere eadem methodologia utens?\u201d Tibi magnopere suadeo ut coneris eas in ordine diverso perficere atque unaquaque demonstratione ad sequentes progrediaris, nam etiamsi non succedat, ipsa praxis conatus maiorem intelligentiam demonstrationum et methodorum logicorum tibi praebebit.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Leges DeMorgan, Distributionis earumque Demonstrationes SUMMARIUMIn hac lectione tractantur demonstrationes legum DeMorgan et distributionis coniunctionis ac disiunctionis, quae frequenter in logica propositionali adhibentur necnon in disciplinis talibus quales sunt theoria congregationum, probabilitates, topologia, electronica et programmatio. Exponuntur aequivalentiae quae distributionem negationum cum coniunctione et disiunctione formaliter exprimunt, sicut etiam regulas distributivitatis inter coniunctionem et disiunctionem. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27484,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":27,"footnotes":""},"categories":[1352,1358,1298],"tags":[],"class_list":["post-33853","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-logica-mathematica","category-logica-propositionalis","category-mathematica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Leges DeMorgan, Distributionis earumque Demonstrationes - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.\" \/>\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\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Leges DeMorgan, Distributionis earumque Demonstrationes\" \/>\n<meta property=\"og:description\" content=\"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/\" \/>\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=\"2021-02-14T15:00:05+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-07-31T23:23:06+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Leges DeMorgan, Distributionis earumque Demonstrationes\" \/>\n<meta name=\"twitter:description\" content=\"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.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=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Leges DeMorgan, Distributionis earumque Demonstrationes\",\"datePublished\":\"2021-02-14T15:00:05+00:00\",\"dateModified\":\"2025-07-31T23:23:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/\"},\"wordCount\":1252,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/demorgan.jpg\",\"articleSection\":[\"Logica Mathematica\",\"Logica Propositionalis\",\"Mathematica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/\",\"name\":\"Leges DeMorgan, Distributionis earumque Demonstrationes - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#primaryimage\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/demorgan.jpg\",\"datePublished\":\"2021-02-14T15:00:05+00:00\",\"dateModified\":\"2025-07-31T23:23:06+00:00\",\"description\":\"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#primaryimage\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/demorgan.jpg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/demorgan.jpg\",\"width\":1024,\"height\":356,\"caption\":\"Created with GIMP\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/leges-demorgan-distributionis-earumque-demonstrationes\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Leges DeMorgan, Distributionis earumque Demonstrationes\"}]},{\"@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":"Leges DeMorgan, Distributionis earumque Demonstrationes - toposuranos.com\/material","description":"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.","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\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/","og_locale":"es_ES","og_type":"article","og_title":"Leges DeMorgan, Distributionis earumque Demonstrationes","og_description":"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.","og_url":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-02-14T15:00:05+00:00","article_modified_time":"2025-07-31T23:23:06+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"Leges DeMorgan, Distributionis earumque Demonstrationes","twitter_description":"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"Leges DeMorgan, Distributionis earumque Demonstrationes","datePublished":"2021-02-14T15:00:05+00:00","dateModified":"2025-07-31T23:23:06+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/"},"wordCount":1252,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.jpg","articleSection":["Logica Mathematica","Logica Propositionalis","Mathematica"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/","url":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/","name":"Leges DeMorgan, Distributionis earumque Demonstrationes - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.jpg","datePublished":"2021-02-14T15:00:05+00:00","dateModified":"2025-07-31T23:23:06+00:00","description":"Disce Leges DeMorgan atque regulas distributivitatis in logica propositionali. Per earum demonstrationes naturam earum penitus intelleges.","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/demorgan.jpg","width":1024,"height":356,"caption":"Created with GIMP"},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/la\/leges-demorgan-distributionis-earumque-demonstrationes\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"Leges DeMorgan, Distributionis earumque Demonstrationes"}]},{"@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\/33853","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=33853"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/33853\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/27484"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=33853"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=33853"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=33853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}