{"id":55225,"date":"2014-08-25T02:09:27","date_gmt":"2014-08-24T18:09:27","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=55225"},"modified":"2021-10-06T16:15:20","modified_gmt":"2021-10-06T08:15:20","slug":"%e6%95%b8%e5%ad%b8%e6%95%98%e8%bf%b0%e8%88%87%e9%82%8f%e8%bc%af%e9%80%a3%e8%a9%9e-mathematical-statements-and-connectives","status":"publish","type":"post","link":"http:\/\/localhost\/%e6%95%b8%e5%ad%b8%e6%95%98%e8%bf%b0%e8%88%87%e9%82%8f%e8%bc%af%e9%80%a3%e8%a9%9e-mathematical-statements-and-connectives\/","title":{"rendered":"\u6578\u5b78\u6558\u8ff0\u8207\u908f\u8f2f\u9023\u8a5e (Mathematical statements and connectives)"},"content":{"rendered":"

\u6578\u5b78\u6558\u8ff0\u8207\u908f\u8f2f\u9023\u8a5e (Mathematical statements and connectives)<\/strong><\/span>
\n\u81fa\u5317\u5e02\u7acb\u548c\u5e73\u9ad8\u4e2d\u9ec3\u4fca\u744b\u6559\u5e2b<\/strong><\/span><\/p>\n

\u5982\u3008\u6578\u5b78\u6558\u8ff0\u8207\u908f\u8f2f\u91cf\u8a5e<\/a>\u3009\u4e00\u6587\u6240\u8ff0\uff0c\u4e00\u822c\u6578\u5b78\u6558\u8ff0\u4e3b\u8981\u90fd\u662f\u4e0b\u5217\u56db\u7a2e\u578b\u5f0f\u6216\u5176\u5426\u5b9a\u578b\u614b\uff1a<\/p>\n

(1) \u7269\u4ef6 \\(a\\)\u00a0\u5177\u6709\u6027\u8cea \\(P\\)\u3002
\n(2) \\(T\\)\u00a0<\/i>\u985e\u4e2d\u7684\u6bcf\u500b\u7269\u4ef6\uff0c\u90fd\u5177\u6709\u6027\u8cea \\(P\\)\u3002
\n(3) \u5b58\u5728\u4e00\u500b \\(T\\)\u00a0<\/i>\u985e\u4e2d\u7269\u4ef6\uff0c\u5177\u6709\u6027\u8cea \\(P\\)\u3002
\n(4) \u82e5\u6558\u8ff0 \\(A\\)\u00a0<\/i>\u5247\u6558\u8ff0 \\(B\\)\u3002<\/p>\n

\u6709\u4e86\u9019\u56db\u985e\u6558\u8ff0\u53e5\u4e4b\u5f8c\uff0c\u52a0\u4e0a\u908f\u8f2f\u9023\u8a5e\u300c\u4e14\u300d\u3001\u300c\u6216\u300d\u8207\u300c\u975e\u300d\u4e4b\u5f8c\uff0c\u4fbf\u80fd\u9020\u51fa\u65b0\u7684\u6558\u8ff0\u53e5\u3002<\/p>\n

\u4e00\u822c\u800c\u8a00\uff0c\u6211\u5011\u6703\u4ee5\u7b26\u865f\u300c\\(\\land\\)\u300d\u4ee3\u8868\u300c\u4e14\u300d\u7684\u610f\u601d\uff1b\u4ee5\u7b26\u865f\u300c\\(\\lor\\)\u300d\u4ee3\u8868\u300c\u6216\u300d\u7684\u610f\u601d\u3002<\/p>\n

\u5176\u4e2d\uff0c\\(P\\land Q\\)\u00a0\u7684\u610f\u601d\u662f \\(P\\)\u00a0\u8207 \\(Q\\)\u00a0\u540c\u6642\u6210\u7acb\uff0c\\(P\\land Q\\)\u00a0\u4e5f\u88ab\u7a31\u70ba\u6558\u8ff0 \\(P\\)\u00a0\u8207\u6558\u8ff0 \\(Q\\)\u00a0\u7684\u5408\u53d6\u53e5(conjunctions)\u3002\u5fc5\u9700\u6eff\u8db3 \\(P\\)\u00a0\u8207 \u00a0\\(Q\\)\u00a0\u540c\u6642\u70ba\u771f\uff0c\u6558\u8ff0\u53e5 \\(P\\land Q\\)\u00a0\u65b9\u70ba\u771f\u3002<\/p>\n

\u4f8b\u5982(\\(\\pi\\) \u662f\u5be6\u6578)\\(\\land\\)(\\(2\\) \u662f\u8cea\u6578)\u6b64\u547d\u984c\u5373\u70ba\u771f\uff0c\u800c(\\(\\pi\\) \u662f\u6709\u7406\u6578)\\(\\land\\)(\\(2\\) \u662f\u8cea\u6578)\u5247\u70ba\u5047\u3002<\/p>\n

<\/p>\n

\u63a5\u4e0b\u4f86\uff0c\u6211\u5011\u5f15\u5165\u4e00\u7a2e\u7a31\u70ba\u300c\u908f\u8f2f\u771f\u503c\u8868\u300d\u7684\u8868\u683c\uff0c\u4f5c\u9032\u4e00\u6b65\u6574\u7406\uff08\u5982\u8868\u4e00\u6240\u793a\uff09\u3002\u5176\u4e2d\uff0c\u6211\u5011\u4ee5\u300c\\(T\\)\u300d\u6307\u7a31\u8a72\u547d\u984c\u70ba\u300c\u771f\u300d\uff0c\u4ee5\u300c\\(F\\)\u300d\u6307\u7a31\u8a72\u547d\u984c\u70ba\u300c\u5047\uff08\u507d\uff09\u300d\u3002\u6b64\u8868\u8aaa\u660e\u4e86\uff0c\u6558\u8ff0 \\(P\\)\u00a0\u8207\u6558\u8ff0 \\(Q\\)\u00a0\u4e4b\u771f\u5047\u503c\uff0c\u8207\u5176\u5408\u53d6\u53e5 \\(P\\land Q\\)\u00a0\u4e4b\u771f\u5047\u503c\u4e4b\u9593\u7684\u95dc\u4fc2\u3002<\/p>\n

\"55225_c1\"<\/a>

\u8868\u4e00 \\(P\\land Q\\)\u00a0\u4e4b\u908f\u8f2f\u771f\u503c\u8868<\/p><\/div>\n

\u53e6\u4e00\u65b9\u9762\uff0c\\(P\\lor Q\\)\u00a0\u7684\u610f\u601d\u662f \\(P\\)\u00a0\u70ba\u771f\u6216 \\(Q\\)\u00a0\u70ba\u771f\uff0c\u6578\u5b78\u8207\u908f\u8f2f\u4e0a\u7684\u300c\u6216\u300d\u8207\u4e00\u822c\u65e5\u5e38\u8a9e\u8a00\u4e2d\u7684\u6163\u7528\u65b9\u5f0f\u6709\u6240\u4e0d\u540c\uff0c\u9019\u88e1\u6211\u5011\u9650\u5236\u5176\u70ba\u300c\u76f8\u5bb9\u7684\u6216\u300d\uff0c\u63db\u53e5\u8a71\u8aaa\uff0c\u9019\u500b\u6558\u8ff0\u53e5\u5305\u542b\u4e86\u4e09\u7a2e\u60c5\u6cc1\uff1a<\/p>\n

\\(P\\)\u00a0\u6558\u8ff0\u70ba\u771f\u4e14 \\(Q\\)\u00a0\u6558\u8ff0\u70ba\u5047\u3001\\(P\\)\u00a0\u6558\u8ff0\u70ba\u771f\u4e14 \\(Q\\)\u00a0\u6558\u8ff0\u70ba\u5047\u4ee5\u53ca \\(P\\)\u00a0\u6558\u8ff0\u8207 \\(Q\\)\u00a0\u6558\u8ff0\u540c\u6642\u70ba\u771f\u3002<\/p>\n

\u800c \\(P\\lor Q\\)\u00a0\u4e5f\u88ab\u7a31\u70ba \\(P\\)\u00a0\u6558\u8ff0\u8207 \\(Q\\)\u00a0\u6558\u8ff0\u7684\u6790\u53d6\u53e5(disjunctions)\uff0c\u53ea\u8981 \\(P\\)\u00a0\u8207 \\(Q\\)\u00a0\u5176\u4e2d\u4e4b\u4e00\u70ba\u771f\uff0c\u5247\u6574\u500b\u6790\u53d6\u53e5 \\(P\\lor Q\\)\u00a0\u5373\u70ba\u771f\u3002<\/p>\n

\u4f8b\u5982(\\(\\pi\\) \u662f\u5be6\u6578)\\(\\lor\\)(\\(2\\) \u662f\u8cea\u6578)\u8207(\\(\\pi\\) \u662f\u6574\u6578)\\(\\lor\\)(\\(2\\) \u662f\u8cea\u6578)\u4ee5\u53ca(\\(\\pi\\)\u00a0\u662f\u7121\u7406\u6578)\\(\\lor\\)(\\(2\\)\u00a0\u662f\u5b8c\u5168\u5e73\u65b9\u6578)<\/p>\n

\u9019\u88e1\uff0c\u6211\u5011\u540c\u6a23\u5229\u7528\u300c\u908f\u8f2f\u771f\u503c\u8868\u300d\uff08\u5982\u8868\u4e8c\u6240\u793a\uff09\uff0c\u6574\u7406\u6558\u8ff0 \\(P\\) \u8207\u6558\u8ff0 \\(Q\\) \u4e4b\u771f\u5047\u503c\uff0c\u8207\u5176\u6790\u53d6\u53e5 \\(P\\lor Q\\) \u4e4b\u771f\u5047\u503c\u4e4b\u9593\u7684\u95dc\u4fc2\u3002<\/p>\n

\"55225_c2\"<\/a>

\u8868\u4e8c \\(P\\lor Q\\) \u4e4b\u908f\u8f2f\u771f\u503c\u8868<\/p><\/div>\n

\u6700\u5f8c\u4e00\u985e\u908f\u8f2f\u9023\u8a5e\u300c\u975e\u300d\uff0c\u5247\u5177\u6709\u5426\u5b9a\u7684\u610f\u601d\uff0c\u5176\u7528\u4ee5\u5ba3\u544a\u67d0\u500b\u7279\u5b9a\u7684\u6558\u8ff0\u53e5\u70ba\u5047\u3002\u4f8b\u5982\uff0c\\(P\\) \u662f\u67d0\u4e00\u6558\u8ff0\u53e5\uff0c\u5247\u975e \\(P\\) \u5373\u70ba \\(P\\) \u7684\u5426\u5b9a\u6558\u8ff0\u53e5\u3002\u5176\u4e2d\uff0c\u82e5 \\(P\\) \u70ba\u771f\uff0c\u5247\u975e \\(P\\) \u70ba\u5047\uff0c\u53cd\u4e4b\uff0c\u82e5 \\(P\\) \u70ba\u5047\uff0c\u5247\u975e \\(P\\) \u70ba\u771f\u3002<\/p>\n

\u4e00\u822c\u6211\u5011\u6703\u4ee5\u7b26\u865f\u300c\\(\\neg\\)\u300d\u4f86\u8868\u793a\u300c\u975e\u300d\u7684\u610f\u601d\u3002\u800c\u9023\u63a5\u8a5e\u300c\u975e\u300d\u7684\u76f8\u95dc\u300c\u908f\u8f2f\u771f\u503c\u8868\u300d\uff0c\u5247\u5982\u8868\u4e09\u6240\u793a\uff1a<\/p>\n

\"55225_c3\"<\/a>

\u8868\u4e09 \\(\\neg P\\)\u00a0\u4e4b\u908f\u8f2f\u771f\u503c\u8868<\/p><\/div>\n

\u7576\u6211\u5011\u9032\u4e00\u6b65\u52a0\u4e0a\u300c\u6240\u6709\u300d\u3001\u300c\u5b58\u5728\u300d\u7b49\u908f\u8f2f\u91cf\u8a5e\u6642\uff0c\u6578\u5b78\u6558\u8ff0\u7684\u5426\u5b9a\u6703\u8b8a\u5f97\u7a0d\u52a0\u8907\u96dc\u3002\u82e5\u6709\u4eba\u5ba3\u7a31\uff1a\u300c\u6240\u6709\u7684\u8cea\u6578\u90fd\u662f\u5947\u6578\u300d\u6642\uff0c\u6b64\u6558\u8ff0\u986f\u7136\u70ba\u507d\uff0c\u7136\u800c\uff0c\u5b83\u7684\u5426\u5b9a\u6558\u8ff0\u662f\u4ec0\u9ebc\u5462\uff1f
\n\u63db\u53e5\u8a71\u8aaa\uff0c\u6211\u5011\u8a72\u5982\u4f55\u9069\u7576\u5730\u300c\u5426\u5b9a\u300d\u5b83\u3001\u4fee\u6539\u5b83\uff0c\u4f7f\u5b83\u70ba\u771f\u5462\uff1f\u4ee5\u4e0b\u63d0\u51fa\u56db\u7a2e\u53ef\u80fd\u65b9\u6848\uff1a<\/p>\n

(1) \u6240\u6709\u7684\u8cea\u6578\u90fd\u662f\u5076\u6578\u3002
\n(2) \u6240\u6709\u7684\u8cea\u6578\u90fd\u4e0d\u662f\u5947\u6578\u3002
\n(3) \u5b58\u5728\u81f3\u5c11\u6709\u4e00\u500b\u8cea\u6578\u662f\u5076\u6578\u3002
\n(4) \u5b58\u5728\u81f3\u5c11\u6709\u4e00\u500b\u8cea\u6578\u4e0d\u662f\u5947\u6578\u3002<\/p>\n

\u4e4d\u770b\u4e4b\u4e0b\uff0c\u4e5f\u8a31\u521d\u5b78\u8005\u6216\u8005\u5c0d\u4e0d\u61c2\u57fa\u790e\u6578\u8ad6\u7684\u4eba\uff0c\u6703\u8a8d\u70ba(1)\u8207(2)\u662f\u5408\u9069\u7684\u7b54\u6848\uff0c\u4e0d\u904e\u4ed4\u7d30\u4e00\u60f3\uff0c\u6558\u8ff0\u53e5(1)\u660e\u986f\u4e0d\u70ba\u771f\uff0c\u7136\u800c\uff0c\u539f\u6558\u8ff0\u53e5\u70ba\u5047\uff0c\u5176\u5426\u5b9a\u6558\u8ff0\u5fc5\u70ba\u771f\uff0c\u56e0\u6b64\uff0c\u6558\u8ff0(1)\u4e26\u975e\u6211\u5011\u6240\u8981\u7684\u7b54\u6848\u3002\u81f3\u65bc(2)\u5462\uff1f\u6240\u6709\u7684\u8cea\u6578\u90fd\u4e0d\u662f\u5947\u6578\uff0c\u6b64\u6558\u8ff0\u53e5\u4ea6\u70ba\u5047\uff0c\u56e0\u6b64\uff0c\u5b83\u4e5f\u4e0d\u53ef\u80fd\u662f\u539f\u6558\u8ff0\u7684\u5426\u5b9a\u6558\u8ff0\u3002\u90a3\u6558\u8ff0(3)\u53c8\u5982\u4f55\uff1f\u6b64\u6558\u70ba\u771f\uff0c\u4f8b\u59822\u9019\u500b\u8cea\u6578\u4fbf\u662f\u5076\u6578\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6558\u8ff0(4)\u540c\u6a23\u70ba\u771f\uff0c\u56e0\u70ba2\u9019\u500b\u8cea\u6578\u4e0d\u662f\u5947\u6578\uff0c\u4e0d\u904e\u7a76\u7adf\u6558\u8ff0(3)\u8207\u6558\u8ff0(4)\uff0c\u4f55\u8005\u624d\u662f\u539f\u6558\u8ff0\u6bd4\u8f03\u6070\u7576\u7684\u5426\u5b9a\u5462\uff1f<\/p>\n

\u4e8b\u5be6\u4e0a\uff0c\u9019\u5169\u500b\u6558\u8ff0\u90fd\u5448\u73fe\u51fa\u539f\u6558\u8ff0\u300c\u6240\u6709\u7684\u8cea\u6578\u90fd\u662f\u5947\u6578\u300d\u7684\u5426\u5b9a\u72c0\u614b\uff0c\u63db\u8a00\u4e4b\uff0c\u82e5\u6211\u5011\u8981\u5426\u5b9a\u300c\u6240\u6709\u7684\u8cea\u6578\u90fd\u662f\u5947\u6578\u300d\uff0c\u53ef\u4ee5\u5229\u7528\u627e\u5230\u4e00\u500b\u53cd\u4f8b\u7684\u65b9\u5f0f\uff1a\u5373\u5229\u7528\u5b58\u5728\u81f3\u5c11\u4e00\u500b\u8cea\u6578\u4e0d\u662f\u5947\u6578\uff0c\u4f86\u5426\u5b9a\u539f\u6558\u8ff0\u3002\u540c\u6642\uff0c\u5728\u6578\u5b78\u7684\u9818\u57df\u88e1\uff08\u7279\u5225\u662f\u6574\u6578\u8ad6\u88e1\uff09\uff0c\u4e0d\u662f\u5947\u6578\u4e4b\u5426\u5b9a\uff0c\u5373\u70ba\u5076\u6578\uff0c\u56e0\u6b64\uff0c\u6558\u8ff0(3)\u8207\u6558\u8ff0(4)\u90fd\u662f\u539f\u6558\u8ff0\u7684\u5426\u5b9a\u3002<\/p>\n

\u4e00\u822c\u800c\u8a00\uff0c\u300c\\(\\forall x\\)\uff0c\u7686\u6eff\u8db3\u6027\u8cea \\(P\\)\u300d\u7684\u5426\u5b9a\u6558\u8ff0\u5373\u70ba\u300c\\(\\exists x\\)\uff0c\u4e0d\u6eff\u8db3\u6027\u8cea \\(P\\)\u300d\u6216\u300c\\(\\exists x\\)\uff0c\u6eff\u8db3\u6027\u8cea \\(\\neg P\\)\u300d\u3002\u985e\u4f3c\u5730\uff0c\u6211\u5011\u4e5f\u53ef\u77e5\u300c\\(\\exists x\\)\uff0c\u6eff\u8db3\u6027\u8cea \\(P\\)\u300d\u7684\u5426\u5b9a\u6558\u8ff0\u5373\u70ba\u300c\\(\\forall x\\)\uff0c\u4e0d\u6eff\u8db3\u6027\u8cea \\(P\\)\u300d\u6216\u300c\\(\\forall x\\)\uff0c\u6eff\u8db3\u6027\u8cea \\(\\neg P\\)\u300d\u3002<\/p>\n

\u53c3\u8003\u6587\u737b\uff1a<\/p>\n

    \n
  • \u9f4a\u65af\uff0e\u5fb7\u798f\u6797\uff08Keith Devlin\uff09\u8457\uff08\u6d2a\u842c\u751f\u3001\u9ec3\u4fca\u744b\u7b49\u8b6f\uff09\uff0c\u300a\u9019\u500b\u554f\u984c\uff0c\u4f60\u7528\u6578\u5b78\u65b9\u5f0f\u60f3\u904e\u55ce\uff1f\u300b<\/li>\n<\/ul>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u6578\u5b78\u6558\u8ff0\u8207\u908f\u8f2f\u9023\u8a5e (Mathematical statements and connectives) \u81fa\u5317\u5e02…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111,215],"tags":[6890,348,6891],"class_list":["post-55225","post","type-post","status-publish","format-standard","hentry","category-mathematics00","category-math01","tag-6890","tag-348","tag-6891","loop-entry","cat-111","cat-215","no-thumbnail"],"views":10460,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/55225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=55225"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/55225\/revisions"}],"predecessor-version":[{"id":86945,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/55225\/revisions\/86945"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=55225"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=55225"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=55225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}