{"id":27492,"date":"2021-02-14T13:00:16","date_gmt":"2021-02-14T13:00:16","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27492"},"modified":"2024-07-18T21:37:36","modified_gmt":"2024-07-18T21:37:36","slug":"%e5%be%b7%e6%91%a9%e6%a0%b9%e5%ae%9a%e5%be%8b%e3%80%81%e5%88%86%e9%85%8d%e5%be%8b%e5%8f%8a%e5%85%b6%e8%af%81%e6%98%8e","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e5%be%b7%e6%91%a9%e6%a0%b9%e5%ae%9a%e5%be%8b%e3%80%81%e5%88%86%e9%85%8d%e5%be%8b%e5%8f%8a%e5%85%b6%e8%af%81%e6%98%8e\/","title":{"rendered":"\u5fb7\u6469\u6839\u5b9a\u5f8b\u3001\u5206\u914d\u5f8b\u53ca\u5176\u8bc1\u660e"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u5fb7\u6469\u6839\u5b9a\u5f8b\u3001\u5206\u914d\u5f8b\u53ca\u5176\u8bc1\u660e<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u56de\u987e\u4e86\u5fb7\u6469\u6839\u5b9a\u5f8b\u7684\u5408\u53d6\u4e0e\u6790\u53d6\u5206\u914d\u5f8b\u7684\u8bc1\u660e\uff0c\u8fd9\u4e9b\u5b9a\u5f8b\u5728\u547d\u9898\u903b\u8f91\u548c\u8bf8\u5982\u96c6\u5408\u8bba\u3001\u6982\u7387\u8bba\u3001\u62d3\u6251\u5b66\u3001\u7535\u5b50\u5b66\u548c\u7f16\u7a0b\u7b49\u9886\u57df\u4e2d\u7ecf\u5e38\u4f7f\u7528\u3002\u4ecb\u7ecd\u4e86\u5f62\u5f0f\u5316\u63cf\u8ff0\u5426\u5b9a\u4e0e\u5408\u53d6\u548c\u6790\u53d6\u5206\u914d\u7684\u7b49\u4ef7\u5f0f\uff0c\u4ee5\u53ca\u5408\u53d6\u548c\u6790\u53d6\u4e4b\u95f4\u7684\u5206\u914d\u89c4\u5219\u3002\u89e3\u91ca\u4e86\u7528\u4e8e\u83b7\u5f97\u8fd9\u4e9b\u8bc1\u660e\u7684\u6f14\u7ece\u6280\u672f\uff0c\u5e76\u9f13\u52b1\u5b66\u751f\u5b8c\u6210\u6240\u63d0\u8bae\u7684\u8bc1\u660e\u4ee5\u5f3a\u5316\u4ed6\u4eec\u7684\u77e5\u8bc6\u3002\u8fd8\u5efa\u8bae\u8fdb\u884c\u8fd9\u6837\u4e00\u4e2a\u7ec3\u4e60\uff1a\u201c\u6211\u80fd\u5426\u6309\u7167\u76f8\u540c\u7684\u65b9\u6cd5\u4ee5\u4e0d\u540c\u7684\u987a\u5e8f\u6784\u5efa\u8fd9\u4e9b\u8bc1\u660e\uff1f\u201d\u4ee5\u63d0\u9ad8\u903b\u8f91\u6280\u80fd\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\n<\/p>\n<ol>\n<li><strong>\u8bc1\u660e<\/strong>\u5fb7\u6469\u6839\u5b9a\u5f8b\u548c\u5408\u53d6\u4e0e\u6790\u53d6\u4e4b\u95f4\u7684\u5206\u914d\u89c4\u5219\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u6240\u5b66\u7684\u6f14\u7ece\u6280\u672f\u6765\u8bc1\u660e\u5fb7\u6469\u6839\u5b9a\u5f8b\u548c\u5206\u914d\u5f8b\u3002<\/li>\n<li><strong>\u6bd4\u8f83<\/strong>\u5fb7\u6469\u6839\u5b9a\u5f8b\u548c\u5206\u914d\u5f8b\u7684\u8bc1\u660e\uff0c\u5bfb\u627e\u76f8\u4f3c\u70b9\u548c\u4e0d\u540c\u70b9\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong>\u5fb7\u6469\u6839\u5b9a\u5f8b\u548c\u5206\u914d\u5f8b\u7684\u8bc1\u660e\uff0c\u4ee5\u63d0\u9ad8\u5bf9\u547d\u9898\u903b\u8f91\u7684\u7406\u89e3\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u76ee\u5f55<\/strong><br \/>\n<a href=\"#1\">\u5fb7\u6469\u6839\u5b9a\u5f8b<\/a><br \/>\n<a href=\"#2\">\u5408\u53d6\u4e0e\u6790\u53d6\u4e4b\u95f4\u7684\u5206\u914d\u89c4\u5219<\/a><br \/>\n<a href=\"#2\">\u6700\u540e\u7684\u8003\u8651<\/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; color: #000000;\">\u73b0\u5728\u662f\u65f6\u5019\u56de\u987e\u547d\u9898\u903b\u8f91\u4e2d\u53e6\u4e00\u79cd\u7ecf\u5e38\u4f7f\u7528\u7684\u6027\u8d28\uff0c\u5373\u5fb7\u6469\u6839\u5b9a\u5f8b\u7684\u5408\u53d6\u548c\u6790\u53d6\u5206\u914d\u8bc1\u660e\u3002\u8fd9\u4e9b\u5b9a\u5f8b\u5728\u96c6\u5408\u8bba\u4e2d\u5f88\u5e38\u7528\uff0c\u8fdb\u800c\u5f71\u54cd\u6574\u4e2a\u6570\u5b66\uff1a\u4ece\u6982\u7387\u8bba\u3001\u62d3\u6251\u5b66\u5230\u7535\u5b50\u5b66\u548c\u7f16\u7a0b\u3002\u50cf\u5f80\u5e38\u4e00\u6837\uff0c\u6211\u4eec\u5c06\u4ece\u5df2\u7ecf\u638c\u63e1\u7684\u6f14\u7ece\u6280\u672f\u4e2d\u8be6\u7ec6\u89e3\u6790\u8fd9\u4e9b\u5b9a\u5f8b\u7684\u8bc1\u660e\u3002<\/p>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u5fb7\u6469\u6839\u5b9a\u5f8b<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=709s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5fb7\u6469\u6839\u5b9a\u5f8b<\/span><\/strong><\/a>\u662f\u4e00\u7ec4\u7b49\u4ef7\u5f0f\uff0c\u5f62\u5f0f\u5316\u63cf\u8ff0\u4e86\u5426\u5b9a\u4e0e\u5408\u53d6\u548c\u6790\u53d6\u7684\u5206\u914d\u3002\u5f62\u5f0f\u4e0a\uff0c\u901a\u8fc7\u4ee5\u4e0b\u7b49\u4ef7\u5f0f\u8868\u793a\uff1a<\/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; color: #000000;\">\u8fd9\u4e9b\u5df2\u7ecf\u8bc1\u660e\u7684\u7b49\u4ef7\u5f0f\u53ef\u4ee5\u4e0d\u9700\u8981\u50cf\u6211\u4eec\u4ee5\u524d\u90a3\u6837\u8fdb\u884c\u8bc1\u660e\uff0c\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5408\u53d6\u548c\u6790\u53d6\u4e4b\u95f4\u7684\u5b9a\u4e49\u4ee5\u53ca\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7\u548c\u66ff\u6362\u7684\u4e00\u4e9b\u6280\u5de7\u3002\u4ece\u5408\u53d6\u7684\u5b9a\u4e49\u53ef\u4ee5\u5f97\u51fa\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u5c06\u8fd9\u8868\u8fbe\u5f0f\u4e24\u8fb9\u90fd\u53d6\u53cd\uff0c\u6211\u4eec\u5f97\u5230<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u7136\u540e\uff0c\u901a\u8fc7\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7\uff0c\u6211\u4eec\u5f97\u5230<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u6700\u540e\uff0c\u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=\\alpha<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B=\\beta<\/span><\/span>\uff0c\u6211\u4eec\u5f97\u5230\u5fb7\u6469\u6839\u7684\u7b2c\u4e00\u4e2a\u7b49\u4ef7\u5f0f<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u4e3a\u4e86\u5f97\u5230\u7b2c\u4e8c\u4e2a\u7b49\u4ef7\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u7ee7\u7eed\u64cd\u4f5c\uff0c\u5c06\u4e4b\u524d\u8868\u8fbe\u5f0f\u4e24\u8fb9\u518d\u53d6\u53cd\uff0c\u5f97\u5230<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u7136\u540e\uff0c\u901a\u8fc7\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7\uff0c\u6211\u4eec\u5f97\u5230<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u5728\u8fd9\u4e2a\u6700\u540e\u8868\u8fbe\u5f0f\u4e2d\uff0c\u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=\\neg\\alpha<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B=\\neg\\beta<\/span><\/span>\uff0c\u6211\u4eec\u5c06\u5f97\u5230<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u7531\u4e8e\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7\uff0c\u8fd9\u5c06\u5bfc\u81f4\u5fb7\u6469\u6839\u7684\u7b2c\u4e8c\u4e2a\u7b49\u4ef7\u5f0f<\/p>\n<p style=\"text-align: center; color: #000000;\"><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; color: #000000;\">\u6b64\u5916\uff0c\u4ee5\u5b8c\u5168\u7c7b\u4f3c\u7684\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u83b7\u5f97\u4e00\u4e9b\u989d\u5916\u7684\u5f62\u5f0f\uff0c\u8fd9\u4e9b\u53ea\u662f\u6211\u4eec\u521a\u521a\u56de\u987e\u8fc7\u7684\u53d8\u4f53<\/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><\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u7ed3\u5408\u548c\u6790\u53d6\u7684\u5206\u914d\u5f8b\u89c4\u5219<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=709s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u987e\u540d\u601d\u4e49<\/span><\/strong><\/a>\uff0c\u8fd9\u4e9b\u89c4\u5219\u5141\u8bb8\u6211\u4eec\u5728\u8868\u8fbe\u5f0f\u4e2d\u5206\u914d\u96c6\u5408\u548c\u6790\u53d6\u3002\u8fd9\u4e9b\u5b9a\u5f8b\u603b\u7ed3\u5728\u4ee5\u4e0b\u4e24\u4e2a\u7b49\u4ef7\u5173\u7cfb\u4e2d\uff1a<\/p>\n<table style=\"text-align: left; color: #000000;\">\n<tbody>\n<tr>\n<td>\u2227 &#8211; \u5206\u914d\u5f8b<\/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; \u5206\u914d\u5f8b<\/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; color: #000000;\">\u6b63\u5982\u6211\u4eec\u5230\u76ee\u524d\u4e3a\u6b62\u6240\u770b\u5230\u7684\uff0c\u867d\u7136\u8fd9\u662f\u4e00\u4e2a\u5df2\u77e5\u7684\u7ed3\u679c\uff0c\u4f46\u5176\u8bc1\u660e\u5e76\u4e0d\u7b80\u5355\u3002\u5c3d\u7ba1\u4e3a\u4e86\u5b8c\u6210\u8fd9\u4e2a\u8bc1\u660e\u9700\u8981\u53cc\u5411\u63a8\u7406\uff0c\u4f46\u5728\u8fd9\u6b21\u6211\u53ea\u4f1a\u7ed9\u51fa\u4e00\u4e2a\u65b9\u5411\u7684\u8bc1\u660e\uff0c\u53cd\u5411\u7684\u8bc1\u660e\u7559\u7ed9\u8bfb\u8005\u4f5c\u4e3a\u7ec3\u4e60\u3002<\/p>\n<h3>\u2227 &#8211; \u5206\u914d\u5f8b<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=831s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u4e3a\u4e86\u8bc1\u660e\u53d1\u751f\u7684\u60c5\u51b5<\/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> \u8fdb\u884c\u5982\u4e0b\u63a8\u7406\u3002<\/p>\n<table style=\"text-align: left; color: #000000;\">\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>; \u524d\u63d0<\/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-\u6d88\u9664(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>; \u524d\u63d0<\/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-\u5f15\u5165(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-\u5f15\u5165(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>; \u524d\u63d0<\/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-\u6d88\u9664(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>; \u524d\u63d0<\/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-\u6d88\u9664(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-\u6d88\u9664(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-\u5f15\u5165(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-\u5f15\u5165(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>; \u60c5\u51b5\u5206\u6790(5,12)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u6837\u5c31\u8bc1\u660e\u4e86 <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>\u3002\u73b0\u5728\u8f6e\u5230\u4f60\u5c55\u793a\u6240\u5b66\u5e76\u5c1d\u8bd5\u8bc1\u660e <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>\u3002<\/p>\n<h3>\u2228 &#8211; \u5206\u914d\u5f8b<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ntfTrdqIipo&amp;t=1449s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8bc1\u660e<\/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> \u7684\u63a8\u7406\u5982\u4e0b\uff1a<\/p>\n<table style=\"text-align: left; color: #000000;\">\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>; \u524d\u63d0<\/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>; \u524d\u63d0<\/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\\\u03b2 \\wedge\\gamma)), \\neg\\alpha\\}\\vdash (\\beta \\wedge\\gamma)<\/span><\/span><\/td>\n<td>; \u2228-\u6d88\u9664(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-\u6d88\u9664(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-\u6d88\u9664(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>; TD(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>-\u5b9a\u4e49(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>; TD(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>-\u5b9a\u4e49(8)<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/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-\u5f15\u5165(7,9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u53ea\u662f\u8bc1\u660e\u7684\u4e00\u534a\uff0c\u73b0\u5728\u53ea\u9700\u8981\u53cd\u8fc7\u6765\u8bc1\u660e\uff0c\u4f46\u8fd9\u7559\u4f5c\u8bfb\u8005\u7ec3\u4e60 :3<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u6700\u7ec8\u8003\u8651<\/h2>\n<p style=\"text-align: justify; color: #000000;\">\u901a\u8fc7\u6211\u4eec\u5bf9\u5fb7\u6469\u6839\u5b9a\u5f8b\u4e2d\u7ed3\u5408\u4e0e\u6790\u53d6\u7684\u5206\u914d\u5f8b\u8bc1\u660e\u7684\u56de\u987e\uff0c\u6211\u4eec\u53ef\u4ee5\u7ed3\u675f\u5bf9\u547d\u9898\u903b\u8f91\u63a8\u7406\u6280\u672f\u7684\u7814\u7a76\uff0c\u5e76\u4e86\u89e3\u5b83\u4eec\u5982\u4f55\u5728\u7ecf\u5178\u903b\u8f91\u5b9a\u5f8b\uff08\u81f3\u5c11\u662f\u6700\u91cd\u8981\u7684\u5b9a\u5f8b\uff09\u7684\u8bc1\u660e\u4e2d\u6c47\u805a\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5b8c\u6210\u6240\u6709\u5efa\u8bae\u7684\u8bc1\u660e\u5bf9\u4e8e\u5de9\u56fa\u8fd9\u4e9b\u6280\u672f\u7684\u77e5\u8bc6\u975e\u5e38\u91cd\u8981\u3002\u4e3a\u4e86\u8ba9\u8fd9\u7a0d\u5fae\u7b80\u5355\u4e00\u4e9b\uff0c\u975e\u5e38\u6709\u5fc5\u8981\u6bd4\u8f83\u5404\u4e2a\u8bc1\u660e\u4ee5\u5bfb\u627e\u76f8\u4f3c\u4e4b\u5904\uff0c\u56e0\u4e3a\u67d0\u4e9b\u8bc1\u660e\u4e2d\u7684\u7b56\u7565\u53ef\u80fd\u5728\u7a0d\u4f5c\u4fee\u6539\u540e\u9002\u7528\u4e8e\u5176\u4ed6\u8bc1\u660e\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\u4e00\u70b9\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6211\u9009\u62e9\u8fd9\u4e9b\u8bc1\u660e\u7684\u987a\u5e8f\u3002\u4f60\u4f1a\u53d1\u73b0\u6bcf\u4e2a\u8bc1\u660e\u90fd\u4f7f\u7528\u4e86\u4e00\u4e9b\u4e4b\u524d\u8bc1\u660e\u7684\u7ed3\u679c\u3002\u6211\u9009\u62e9\u8fd9\u4e2a\u987a\u5e8f\u662f\u56e0\u4e3a\u5bf9\u6211\u4e2a\u4eba\u800c\u8a00\uff0c\u8fd9\u6837\u66f4\u5bb9\u6613\u3002\u4e00\u4e2a\u63d0\u5347\u8fd9\u4e9b\u6280\u80fd\u7684\u597d\u7ec3\u4e60\u662f\u95ee\u81ea\u5df1\u201c\u6211\u80fd\u5426\u6309\u7167\u4e0d\u540c\u7684\u987a\u5e8f\u7ec4\u7ec7\u8fd9\u4e9b\u8bc1\u660e\u5e76\u9075\u5faa\u76f8\u540c\u7684\u65b9\u6cd5\uff1f\u201d\u6211\u5f3a\u70c8\u5efa\u8bae\u4f60\u5c1d\u8bd5\u6309\u4e0d\u540c\u7684\u987a\u5e8f\u83b7\u5f97\u8fd9\u4e9b\u8bc1\u660e\uff0c\u5e76\u7528\u6bcf\u4e2a\u8bc1\u660e\u6765\u83b7\u5f97\u4e0b\u4e00\u4e2a\uff0c\u56e0\u4e3a\u5373\u4f7f\u4f60\u6ca1\u6709\u6210\u529f\uff0c\u5c1d\u8bd5\u7684\u8fc7\u7a0b\u4e2d\u4ea7\u751f\u7684\u7ec3\u4e60\u4f1a\u8ba9\u4f60\u66f4\u597d\u5730\u7406\u89e3\u8bc1\u660e\u548c\u903b\u8f91\u4e2d\u4f7f\u7528\u7684\u65b9\u6cd5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5fb7\u6469\u6839\u5b9a\u5f8b\u3001\u5206\u914d\u5f8b\u53ca\u5176\u8bc1\u660e \u6458\u8981\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u56de\u987e\u4e86\u5fb7\u6469\u6839\u5b9a\u5f8b\u7684\u5408\u53d6\u4e0e\u6790\u53d6\u5206\u914d\u5f8b\u7684\u8bc1\u660e\uff0c\u8fd9\u4e9b\u5b9a\u5f8b\u5728\u547d\u9898\u903b\u8f91\u548c\u8bf8\u5982\u96c6\u5408\u8bba\u3001\u6982\u7387\u8bba\u3001\u62d3\u6251\u5b66\u3001\u7535\u5b50\u5b66\u548c\u7f16\u7a0b\u7b49\u9886\u57df\u4e2d\u7ecf\u5e38\u4f7f\u7528\u3002\u4ecb\u7ecd\u4e86\u5f62\u5f0f\u5316\u63cf\u8ff0\u5426\u5b9a\u4e0e\u5408\u53d6\u548c\u6790\u53d6\u5206\u914d\u7684\u7b49\u4ef7\u5f0f\uff0c\u4ee5\u53ca\u5408\u53d6\u548c\u6790\u53d6\u4e4b\u95f4\u7684\u5206\u914d\u89c4\u5219\u3002\u89e3\u91ca\u4e86\u7528\u4e8e\u83b7\u5f97\u8fd9\u4e9b\u8bc1\u660e\u7684\u6f14\u7ece\u6280\u672f\uff0c\u5e76\u9f13\u52b1\u5b66\u751f\u5b8c\u6210\u6240\u63d0\u8bae\u7684\u8bc1\u660e\u4ee5\u5f3a\u5316\u4ed6\u4eec\u7684\u77e5\u8bc6\u3002\u8fd8\u5efa\u8bae\u8fdb\u884c\u8fd9\u6837\u4e00\u4e2a\u7ec3\u4e60\uff1a\u201c\u6211\u80fd\u5426\u6309\u7167\u76f8\u540c\u7684\u65b9\u6cd5\u4ee5\u4e0d\u540c\u7684\u987a\u5e8f\u6784\u5efa\u8fd9\u4e9b\u8bc1\u660e\uff1f\u201d\u4ee5\u63d0\u9ad8\u903b\u8f91\u6280\u80fd\u3002 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