{"id":115,"date":"2008-06-11T16:54:44","date_gmt":"2008-06-11T19:54:44","guid":{"rendered":"http:\/\/www.ufrgs.br\/psicoeduc\/?page_id=115"},"modified":"2018-12-07T14:49:53","modified_gmt":"2018-12-07T17:49:53","slug":"a-combinatoria-de-proposicoes","status":"publish","type":"page","link":"https:\/\/www.ufrgs.br\/psicoeduc\/piaget\/a-combinatoria-de-proposicoes\/","title":{"rendered":"A combinat\u00f3ria de proposi\u00e7\u00f5es – Jean Piaget"},"content":{"rendered":"

Fonte:<\/strong> PIAGET, Jean e INHELDER, B\u00e4rbel. A Psicologia da crian\u00e7a<\/em>. S\u00e3o Paulo: Bertrand, 1993.
\nPARRA, N\u00e9lio. O adolescente segundo Piaget<\/em>. S\u00e3o Paulo: Pioneira, 1983.<\/p>\n

Inicialmente temos apenas duas proposi\u00e7\u00f5es \"\" e \"\" que podem ter qualquer conte\u00fado. Por exemplo, podemos dizer que \"\" significa cisne e \"\" significa branco, ou \"\" Gr\u00eamio e \"\" Internacional, etc. Temos tamb\u00e9m a nega\u00e7\u00e3o da proposi\u00e7\u00e3o \"\" (= \"\", n\u00e3o-cisne, n\u00e3o-Gr\u00eamio, etc.) e a nega\u00e7\u00e3o da proposi\u00e7\u00e3o \"\" (= \"\", n\u00e3o-branco, n\u00e3o-Internacional, etc.).<\/p>\n

\"\" = cisne<\/p>\n

\"\" = n\u00e3o-cisne<\/p>\n

\"\" = branco<\/p>\n

\"\" = n\u00e3o-branco<\/p>\n

Podemos combinar essas duas proposi\u00e7\u00f5es (e suas nega\u00e7\u00f5es) de quatro diferentes maneiras:<\/p>\n\n\n\n\n\n\n
\"\" .<\/strong> \"\"<\/td>\ncisne e branco<\/td>\n= a<\/strong><\/td>\n<\/tr>\n
\"\" .<\/strong> \"\"<\/td>\ncisne e n\u00e3o-branco (ex: cisne negro)<\/td>\n= b<\/strong><\/td>\n<\/tr>\n
\"\" .<\/strong> \"\"<\/td>\nn\u00e3o-cisne e branco (ex.: giz, etc.)<\/td>\n= c<\/strong><\/td>\n<\/tr>\n
\"\" .<\/strong> \"\"<\/td>\nn\u00e3o-cisne e n\u00e3o-branco (ex.: giz azul, etc.)<\/td>\n= d<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Denominaremos de a<\/strong>, b<\/strong>, c<\/strong>, e d<\/strong> o resultado da combina\u00e7\u00e3o das duas proposi\u00e7\u00f5es, que, por sua vez, podem ser combinadas de 12 outras diferente maneiras, totalizando 16 combina\u00e7\u00f5es.<\/p>\n

Quadro das 16 opera\u00e7\u00f5es bin\u00e1rias<\/strong><\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
(1) 0<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) Veja errata*<\/span> aqui abaixo.<\/td>\nNega\u00e7\u00e3o<\/td>\n<\/tr>\n
(2) a<\/td>\n( \"\" .<\/strong> \"\" )<\/td>\nConjun\u00e7\u00e3o<\/td>\n<\/tr>\n
(3) b<\/td>\n( \"\" .<\/strong> \"\" )<\/td>\nN\u00e3o-implica\u00e7\u00e3o<\/td>\n<\/tr>\n
(4) c<\/td>\n( \"\" .<\/strong> \"\" )<\/td>\nN\u00e3o-implica\u00e7\u00e3o rec\u00edproca<\/td>\n<\/tr>\n
(5) d<\/td>\n( \"\" .<\/strong> \"\" )<\/td>\nNega\u00e7\u00e3o conjunta<\/td>\n<\/tr>\n
(6) a+b<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nAfirma\u00e7\u00e3o de p<\/td>\n<\/tr>\n
(7) a+c<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nAfirma\u00e7\u00e3o de q<\/td>\n<\/tr>\n
(8) a+d<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nEquival\u00eancia<\/td>\n<\/tr>\n
(9) b+c<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nExclus\u00e3o rec\u00edproca<\/td>\n<\/tr>\n
(10) b+d<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nNega\u00e7\u00e3o de q<\/td>\n<\/tr>\n
(11) c+d<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nNega\u00e7\u00e3o de p<\/td>\n<\/tr>\n
(12) a+b+c<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nDisjun\u00e7\u00e3o<\/td>\n<\/tr>\n
(13) a+b+d<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nImplica\u00e7\u00e3o rec\u00edproca<\/td>\n<\/tr>\n
(14) a+c+d<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nImplica\u00e7\u00e3o<\/td>\n<\/tr>\n
(15) b+c+d<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nIncompatibilidade<\/td>\n<\/tr>\n
(16) a+b+c+d<\/td>\n( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" ) v ( \"\" .<\/strong> \"\" )<\/td>\nAfirma\u00e7\u00e3o completa (tautologia)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

*Errata:<\/span> Verifique o arquivo anexado https:\/\/ufrgs.br\/psicoeduc\/arquivos\/piaget-combinatoria.pdf<\/a> , com a <\/strong>corre\u00e7\u00e3o da representa\u00e7\u00e3o l\u00f3gica da Nega\u00e7\u00e3o, primeira linha do quadro das 16 opera\u00e7\u00f5es bin\u00e1rias.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Fonte: PIAGET, Jean e INHELDER, B\u00e4rbel. A Psicologia da crian\u00e7a. S\u00e3o Paulo: Bertrand, 1993. PARRA, N\u00e9lio. O adolescente segundo Piaget. S\u00e3o Paulo: Pioneira, 1983. Inicialmente temos apenas duas proposi\u00e7\u00f5es e que podem ter qualquer conte\u00fado. Por exemplo, podemos dizer que significa cisne e significa branco, ou Gr\u00eamio e Internacional, etc. Temos tamb\u00e9m a nega\u00e7\u00e3o da … Continue lendo “A combinat\u00f3ria de proposi\u00e7\u00f5es – Jean Piaget”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1063,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-115","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/pages\/115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/comments?post=115"}],"version-history":[{"count":8,"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/pages\/115\/revisions"}],"predecessor-version":[{"id":2497,"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/pages\/115\/revisions\/2497"}],"up":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/pages\/1063"}],"wp:attachment":[{"href":"https:\/\/www.ufrgs.br\/psicoeduc\/wp-json\/wp\/v2\/media?parent=115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}