{"id":33960,"date":"2021-05-09T13:00:44","date_gmt":"2021-05-09T13:00:44","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33960"},"modified":"2025-08-01T04:58:33","modified_gmt":"2025-08-01T04:58:33","slug":"%e6%95%b4%e5%9f%9f%e3%81%a8%e6%95%b4%e6%95%b0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e6%95%b4%e5%9f%9f%e3%81%a8%e6%95%b4%e6%95%b0\/","title":{"rendered":"\u6574\u57df\u3068\u6574\u6570"},"content":{"rendered":"<style>\n\tp, ul, ol{\n\ttext-align: justify;\n\t}\n\th1{\n\ttext-align:center;\n\ttext-transform: uppercase;\n\t}\n\th2{\n\ttext-align:center;\n\ttext-transform: uppercase;\n\tfont-size:24pt;\n\t}\n\th3 { \n\t\ttext-align: center;\n\t\ttext-transform: uppercase;\n\t\tfont-size: 24px !important;\n\t}\n\t<\/style>\n<h1>\u6574\u57df\u3068\u6574\u6570<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u8981\u7d04\uff1a<\/strong><br \/>\n\t\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u6574\u57df\u306e\u6982\u5ff5\u3092\u5c0e\u5165\u3057\u3001\u305d\u308c\u304c\u4e00\u822c\u4ee3\u6570\u5b66\u306e\u7814\u7a76\u306b\u304a\u3044\u3066\u3044\u304b\u306b\u91cd\u8981\u3067\u3042\u308b\u304b\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u5f62\u5f0f\u7684\u8a3c\u660e\u3092\u901a\u3058\u3066\u3001\u305d\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u306e\u3044\u304f\u3064\u304b\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\u3002<\/em><\/p>\n<p>h<\/p>\n<p style=\"text-align:center;\"><em><strong>\u5b66\u7fd2\u76ee\u6a19\uff1a<\/strong><\/em><br \/>\n\t\u672c\u8b1b\u7fa9\u3092\u4fee\u4e86\u3057\u305f\u5b66\u751f\u306f\u4ee5\u4e0b\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a\n\t<\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u4e00\u822c\u4ee3\u6570\u5b66\u306e\u7814\u7a76\u76ee\u7684\u3092\u7406\u89e3\u3059\u308b\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u6574\u57df\u306e\u6982\u5ff5\u3092\u7406\u89e3\u3059\u308b\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong>\uff1a\u6574\u57df\u3068\u6574\u6570\u306b\u5171\u901a\u3059\u308b\u57fa\u672c\u7684\u5074\u9762\u3092\u8aac\u660e\u3059\u308b\u3002<\/li>\n<li><strong>\u8a3c\u660e\u3059\u308b<\/strong>\uff1a\u6574\u57df\u306e\u57fa\u672c\u7684\u6027\u8cea\u3092\u5f62\u5f0f\u7684\u8a3c\u660e\u306b\u3088\u3063\u3066\u793a\u3059\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n\t<strong><u>\u76ee\u6b21<\/u><\/strong><br \/>\n\t<a href=\"#1\">\u4e00\u822c\u4ee3\u6570\u5b66\u306e\u76ee\u7684\u3068\u4e88\u5099\u77e5\u8b58<\/a><br \/>\n\t<a href=\"#2\">\u6574\u6570\u304b\u3089\u6574\u57df\u3078<\/a><br \/>\n\t<a href=\"#3\">\u6574\u57df\u3068\u6574\u6570\u306b\u5171\u901a\u3059\u308b\u57fa\u672c\u7684\u5074\u9762<\/a><br \/>\n\t<a href=\"#4\">\u6574\u57df\u3068\u6574\u6570\u306e\u6027\u8cea<\/a><br \/>\n\t<a href=\"#5\">\u7df4\u7fd2\u554f\u984c<\/a>\n\t<\/p>\n<p>\t<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/hxmc1-eXWxU?si=57GADT52JG4fHFT-\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n\t<\/center><br \/>\n\t<a name=\"1\"><\/a><\/p>\n<h2>\u4e00\u822c\u4ee3\u6570\u5b66\u306e\u76ee\u7684\u3068\u4e88\u5099\u77e5\u8b58<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=183s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u4e00\u822c\u4ee3\u6570\u5b66\u306e\u4e3b\u306a\u76ee\u7684<\/span><\/strong><\/a>\u306f\u3001\u3042\u3089\u3086\u308b\u6570\u5b66\u7684\u4f53\u7cfb\u306e\u591a\u69d8\u6027\u3092\u7814\u7a76\u3059\u308b\u3053\u3068\u306b\u3042\u308a\u307e\u3059\u3002\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u4f53\u7cfb\u3092\u53d6\u308a\u4e0a\u3052\u307e\u3059\u304c\u3001\u7279\u306b\u91cd\u8981\u306a\u306e\u306f\u81ea\u7136\u6570\u3068\u6574\u6570\u3067\u3059\u3002\u3053\u308c\u3089\u3092\u901a\u3057\u3066\u3001\u6700\u7d42\u7684\u306b\u6574\u57df\u3078\u3068\u5230\u9054\u3057\u307e\u3059\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{N}= \\{1,2,3,4,\\cdots\\}<\/span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{Z}= \\{0,\\pm 1,\\pm 2,\\pm 3,\\pm 4,\\cdots\\}<\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u6574\u6570\u304b\u3089\u6574\u57df\u3078<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=358s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u307e\u305a\u306f\u6574\u6570\u306e\u7814\u7a76\u304b\u3089\u59cb\u3081\u307e\u3059\u3002<\/span><\/strong><\/a>\u305d\u306e\u7406\u7531\u306f\u3001\u6574\u6570\u304c\u3053\u308c\u304b\u3089\u672c\u8b1b\u7fa9\u3067\u6271\u3046\u591a\u304f\u306e\u6570\u4f53\u7cfb\u3068\u6700\u3082\u591a\u304f\u306e\u5171\u901a\u70b9\u3092\u6301\u3063\u3066\u3044\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u6574\u6570\u3068\u306f\u4f55\u304b\u3092\u5b9a\u7fa9\u3057\u3088\u3046\u3068\u3059\u308b\u4ee3\u308f\u308a\u306b\u3001\u305d\u308c\u3089\u304c\u3069\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u304b\u3092\u4eee\u5b9a\u3059\u308b\u3068\u3053\u308d\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u6574\u6570\u306b\u76f4\u89b3\u7684\u306b\u95a2\u9023\u3065\u3051\u3089\u308c\u308b\u3059\u3079\u3066\u306e\u6027\u8cea\u304c\u5c0e\u304d\u51fa\u305b\u308b\u3088\u3046\u306a\u4e00\u9023\u306e\u516c\u7406\u3092\u9078\u3073\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u3059\u3079\u3066\u306f\u3001\u81ea\u7136\u6570\u306b\u57fa\u672c\u7684\u306a\u7b97\u8853\u6f14\u7b97\u3092\u5c0e\u5165\u3059\u308b\u969b\u306e<strong>\u30da\u30a2\u30ce\u306e\u516c\u7406<\/strong>\u306b\u3088\u3063\u3066\u884c\u308f\u308c\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u516c\u7406\u7684\u624b\u6cd5\u306b\u5f93\u3044\u3001\u81ea\u7136\u6570\u3084\u6574\u6570\u306b\u6f14\u7b97\u3092\u62e1\u5f35\u3059\u308b\u3053\u3068\u3067\u3001\u6709\u7406\u6570\u3001\u7121\u7406\u6570\u3001\u5b9f\u6570\u3001\u8907\u7d20\u6570\u3001\u56db\u5143\u6570\u3001\u516b\u5143\u6570\u306a\u3069\u306e\u65b0\u3057\u3044\u6570\u4f53\u7cfb\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u6b21\u306b\u3001\u6574\u6570\u306e\u6027\u8cea\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u3059\u3079\u3066\u306e\u4ed6\u306e\u6570\u4f53\u7cfb\u306b\u3082\u5171\u901a\u3057\u3066\u73fe\u308c\u308b\u6027\u8cea\u304c\u3042\u308b\u3053\u3068\u306b\u6c17\u3065\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u4e57\u6cd5\u5358\u4f4d\u5143\u3084\u52a0\u6cd5\u5358\u4f4d\u5143\u3001\u5206\u914d\u6cd5\u5247\u306e\u5b58\u5728\u306a\u3069\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u6027\u8cea\u3092\u524d\u63d0\u3068\u3059\u308b\u3053\u3068\u3067\u3001\u3059\u3079\u3066\u306e\u6570\u4f53\u7cfb\u306b\u3064\u3044\u3066\u5171\u901a\u306e\u8a00\u8a9e\u3067\u8b70\u8ad6\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u6587\u8108\u306b\u304a\u3044\u3066\u3001\u6b21\u306e\u3088\u3046\u306a\u7528\u8a9e\u304c\u73fe\u308c\u307e\u3059\uff1a<\/p>\n<ul>\n<li>\u6574\u57df<\/li>\n<li>\u74b0<\/li>\n<li>\u7fa4<\/li>\n<li>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<\/li>\n<\/ul>\n<p>\u306a\u3069\u3001\u591a\u304f\u306e\u3053\u306e\u7a2e\u306e\u7528\u8a9e\u304c\u767b\u5834\u3057\u307e\u3059\u3002\u672c\u8b1b\u7fa9\u3067\u306f\u307e\u305a<strong>\u6574\u57df<\/strong>\u306e\u7814\u7a76\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u6574\u57df\u3068\u6574\u6570\u306b\u5171\u901a\u3059\u308b\u57fa\u672c\u7684\u6027\u8cea<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=472s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6574\u57df\u3068\u306f\u4f55\u304b\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306b<\/span><\/strong><\/a>\u3001\u79c1\u305f\u3061\u306f\u6574\u6570\u304b\u3089\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b\u6027\u8cea\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u3053\u306e\u6587\u8108\u3067\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> \u304c\u6574\u6570\u3067\u3042\u308b\u3068\u3059\u308b\u3068\u3001\u6b21\u306e<strong>\u6cd5\u5247<\/strong>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/p>\n<ol>\n<li><strong>\u53ef\u63db\u6cd5\u5247\uff1a<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b = b + a<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ab = ba<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li><strong>\u7d50\u5408\u6cd5\u5247\uff1a<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+(b+c) = a+b+c = (a+b)+c<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(ab)c = abc = a(bc)<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li><strong>\u5206\u914d\u6cd5\u5247\uff1a<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+(b+c) = a(b+c) = ab+ac<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p>\u3055\u3089\u306b\u3001\u7279\u5225\u306a\u8981\u7d20\u3068\u3057\u3066\u5358\u4f4d\u5143\u304c\u5b58\u5728\u3057\u307e\u3059\uff1a<\/p>\n<ul>\n<li><strong>\u52a0\u6cd5\u5358\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+ c = a \\leftrightarrow c=0<\/span><\/span><\/li>\n<li><strong>\u4e57\u6cd5\u5358\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ac = a \\leftrightarrow c=1<\/span><\/span><\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u306e\u8a18\u53f7\u3067\u8868\u3055\u308c\u308b\u3082\u306e\u304c\u52a0\u6cd5\u5358\u4f4d\u5143\u3067\u3042\u308a\u3001<span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u306e\u8a18\u53f7\u3067\u8868\u3055\u308c\u308b\u3082\u306e\u304c\u4e57\u6cd5\u5358\u4f4d\u5143\u3067\u3059\u3002<\/p>\n<p>\u6574\u6570\u306f\u307e\u305f\u52a0\u6cd5\u9006\u5143\u3082\u6301\u3061\u307e\u3059\u3002\u4efb\u610f\u306e\u6574\u6570\u306b\u306f\u3001\u52a0\u6cd5\u9006\u5143\u304c\u5b58\u5728\u3057\u3001\u305d\u308c\u3068\u52a0\u3048\u308b\u3068\u52a0\u6cd5\u5358\u4f4d\u5143\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li><strong>\u52a0\u6cd5\u9006\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+ c = 0 \\longleftrightarrow c=-a<\/span><\/span><\/li>\n<\/ul>\n<p>\u52a0\u6cd5\u9006\u5143\u306f\u3001\u305d\u306e\u524d\u306b\u4ed8\u3055\u308c\u305f\u30de\u30a4\u30ca\u30b9\u8a18\u53f7\u300c-\u300d\u306b\u3088\u3063\u3066\u8b58\u5225\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u6700\u5f8c\u306b\u3001<strong>\u7d04\u7c21\u6cd5\u5247<\/strong>\u3068\u547c\u3070\u308c\u308b\u6cd5\u5247\u304c\u5b58\u5728\u3057\u3001\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(c\\neq 0 \\wedge ca = cb) \\longleftrightarrow (a=b)<\/span><\/span><\/p>\n<p>\u3053\u308c\u3089\u306e\u6027\u8cea\u306f\u3001\u5b9f\u6570\u3001\u8907\u7d20\u6570\u3001\u591a\u9805\u5f0f\u306a\u3069\u591a\u304f\u306e\u4ed6\u306e\u96c6\u5408\u306b\u3082\u5f53\u3066\u306f\u307e\u308a\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u3053\u308c\u3089\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u3059\u3079\u3066\u306e\u96c6\u5408\u3092<strong>\u6574\u57df<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n<p><span style=\"color: #800000;\"><strong>\u5b9a\u7fa9\uff1a<\/strong><\/span> \u6574\u57df\u3068\u306f\u3001\u52a0\u6cd5\u304a\u3088\u3073\u4e57\u6cd5\u304c\u5b9a\u7fa9\u3055\u308c\u305f\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u3067\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3082\u306e\u3067\u3059\uff1a<\/p>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in D \\longrightarrow a+b \\in D<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in D \\longrightarrow ab \\in D<\/span><\/span><\/li>\n<\/ul>\n<p>\u3055\u3089\u306b\u3001<strong>\u7d50\u5408\u6cd5\u5247\u3001\u53ef\u63db\u6cd5\u5247<\/strong>\u304a\u3088\u3073<strong>\u5206\u914d\u6cd5\u5247<\/strong>\u304c\u6210\u7acb\u3057\u3001<span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u306f<strong>\u52a0\u6cd5\u5358\u4f4d\u5143<\/strong>\u3068<strong>\u4e57\u6cd5\u5358\u4f4d\u5143<\/strong>\u3092\u542b\u307f\uff08\u3053\u308c\u3089\u306f\u3044\u305a\u308c\u3082\u4e00\u610f\u3067\u3042\u308b\uff09\u3001\u6700\u5f8c\u306b<strong>\u7d04\u7c21\u6cd5\u5247<\/strong>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<h4>\u6574\u57df\u306e\u4f8b<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=749s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=\\{a+b\\sqrt{3}\\; |\\; a,b\\in \\mathbb{Z}\\}<\/span><\/span>\u3068\u3044\u3046\u96c6\u5408\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/span><\/strong><\/a>\u3053\u306e\u96c6\u5408\u306b\u901a\u5e38\u306e\u52a0\u7b97\u304a\u3088\u3073\u4e57\u7b97\u3092\u5b9a\u7fa9\u3059\u308b\u3068\u3001\u3053\u308c\u306f\u6574\u57df\u306b\u306a\u308a\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u3053\u306e\u96c6\u5408\u306f\u53ef\u63db\u6027\u3001\u7d50\u5408\u6027\u3001\u5206\u914d\u6027\u306e\u6cd5\u5247\u3092\u6e80\u305f\u3057\u3001\u52a0\u6cd5\u5358\u4f4d\u5143\u3068\u4e57\u6cd5\u5358\u4f4d\u5143\u3092\u6301\u3061\u3001\u52a0\u6cd5\u9006\u5143\u3082\u5b58\u5728\u3059\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<ul>\n<li><strong>\u52a0\u6cd5\u5358\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0+0\\sqrt{3}<\/span><\/span><\/li>\n<li><strong>\u4e57\u6cd5\u5358\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1+0\\sqrt{3}<\/span><\/span><\/li>\n<li><strong>\u52a0\u6cd5\u9006\u5143\uff1a<\/strong> \u4efb\u610f\u306e\u8981\u7d20 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b\\sqrt{3}<\/span><\/span> \u306b\u5bfe\u3057\u3001\u305d\u306e\u52a0\u6cd5\u9006\u5143\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-a-b\\sqrt{3}<\/span><\/span> \u3067\u3059\u3002<\/li>\n<\/ul>\n<p>\u305d\u3057\u3066\u6700\u3082\u91cd\u8981\u306a\u70b9\u306f\u3001\u3053\u306e\u96c6\u5408 A \u304c\u52a0\u7b97\u3068\u4e57\u7b97\u306b\u95a2\u3057\u3066\u9589\u3058\u3066\u3044\u308b\u3053\u3068\u3067\u3059\u3002\u3064\u307e\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,y\\in A<\/span><\/span> \u3067\u3042\u308c\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x+y\\in A<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">xy\\in A<\/span><\/span> \u3082\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3053\u308c\u306f\u7c21\u5358\u306b\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_1 + b_1\\sqrt{3}<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_2 + b_2\\sqrt{3}<\/span><\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u306e\u8981\u7d20\u3067\u3042\u308c\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text.align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n(a_1 + b_1\\sqrt{3}) + (a_2 + b_2\\sqrt{3}) &amp;=(a_1+a_2) + (b_1 + b_2)\\sqrt{3} \\in A\\\\ \\\\\n\n(a_1 + b_1\\sqrt{3})  (a_2 + b_2\\sqrt{3})  &amp;= a_1a_2 + a_1b_2\\sqrt{3}+b_1a_2\\sqrt{3} + 3b_1b_2 \\\\\n\n&amp;=(a_1a_2 + 3b_1b_2) + (a_1b_2 + b_1a_2)\\sqrt{3} \\in A\n\n\\end{array}<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/y6jXNPhjKv4?si=9SaXhWHN42sC73lZ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u6574\u57df\u3068\u6574\u6570\u306e\u6027\u8cea<\/h3>\n<h4>\u6574\u57df\u306b\u304a\u3051\u308b\u52a0\u6cd5\u5358\u4f4d\u5143\u306e\u4e00\u610f\u6027<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=26s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3053\u308c\u306f\u80cc\u7406\u6cd5\u306b\u3088\u308a\u8a3c\u660e\u3067\u304d\u307e\u3059\uff1a<\/span><\/strong><\/a> \u52a0\u6cd5\u5358\u4f4d\u5143\u304c2\u3064\u5b58\u5728\u3059\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3057\u3087\u3046\u3002\u3059\u306a\u308f\u3061\u3001<span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0^\\prime<\/span><\/span> \u304c\u52a0\u6cd5\u5358\u4f4d\u5143\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; 0\\neq 0^\\prime &amp; \\text{\uff1b \u524d\u63d0}\\\\\n\n(2) &amp; a+0 = a &amp; \\text{\uff1b \u524d\u63d0\uff1a$0$ \u306f\u52a0\u6cd5\u5358\u4f4d\u5143}\\\\\n\n(3) &amp; b+0^\\prime = b &amp; \\text{\uff1b \u524d\u63d0\uff1a$0^\\prime$ \u306f\u52a0\u6cd5\u5358\u4f4d\u5143}\\\\\n\n(4) &amp; 0^\\prime + 0 = 0^\\prime &amp; \\text{\uff1b $(2)$ \u306b $a=0^\\prime$ \u3092\u4ee3\u5165}\\\\\n\n(5) &amp; 0 + 0^\\prime = 0 &amp; \\text{\uff1b $(3)$ \u306b $b=0$ \u3092\u4ee3\u5165}\\\\\n\n(6) &amp; 0 = 0^\\prime  &amp; \\text{\uff1b $(4)$ \u3068 $(5)$ \u3088\u308a\u3001\u52a0\u7b97\u306e\u53ef\u63db\u6027\u3092\u7528\u3044\u308b}\\\\\n\n(7) &amp; \\bot &amp;\\text{\uff1b $(1)$ \u3068 $(6)$ \u306e\u77db\u76fe}\n\n\\end{array}<\/span>\n<p>\u3053\u306e\u63a8\u8ad6\u304b\u3089\u3001\u6b21\u306e\u3053\u3068\u304c\u7d50\u8ad6\u3068\u3057\u3066\u5c0e\u304b\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{0 \\neq 0^\\prime, a + 0 = a, b + 0^\\prime = b\\}\\vdash \\bot.<\/span><\/span><\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u80cc\u7406\u6cd5\u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{a + 0 = a, b + 0^\\prime = b\\}\\vdash 0 = 0^\\prime.<\/span><\/span><\/p>\n<p>\u3064\u307e\u308a\u3001\u3082\u3057\u52a0\u6cd5\u5358\u4f4d\u5143\u304c2\u3064\u5b58\u5728\u3059\u308b\u306a\u3089\u3001\u305d\u308c\u3089\u306f\u7b49\u3057\u304f\u306a\u3051\u308c\u3070\u306a\u3089\u305a\u3001\u3057\u305f\u304c\u3063\u3066\u4e00\u610f\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n<h4>\u4e57\u6cd5\u5358\u4f4d\u5143\u3082\u4e00\u610f\u3067\u3042\u308b<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=305s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3053\u306e\u8a3c\u660e\u306f\u524d\u8ff0\u306e\u3082\u306e\u3068\u307b\u307c\u540c\u69d8\u3067\u3059\u3002<\/span><\/strong><\/a> \u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1^\\prime<\/span><\/span> \u3068\u3044\u30462\u3064\u306e\u4e57\u6cd5\u5358\u4f4d\u5143\u304c\u5b58\u5728\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u63a8\u8ad6\u3067\u304d\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; 1\\neq 1^\\prime &amp; \\text{\uff1b\u524d\u63d0}\\\\\n\n(2) &amp; 1\\cdot a = a &amp; \\text{\uff1b\u524d\u63d0\uff1a$1$ \u306f\u4e57\u6cd5\u5358\u4f4d\u5143}\\\\\n\n(3) &amp; 1^\\prime \\cdot b = b &amp; \\text{\uff1b\u524d\u63d0\uff1a$1^\\prime$ \u306f\u4e57\u6cd5\u5358\u4f4d\u5143}\\\\\n\n(4) &amp; 1\\cdot 1^\\prime = 1^\\prime &amp; \\text{\uff1b$(2)$ \u306b $a=1^\\prime$ \u3092\u4ee3\u5165}\\\\\n\n(5) &amp; 1^\\prime \\cdot 1 = 1 &amp; \\text{\uff1b$(3)$ \u306b $b=1$ \u3092\u4ee3\u5165}\\\\\n\n(6) &amp; 1 = 1^\\prime  &amp; \\text{\uff1b$(4)$ \u3068 $(5)$ \u3088\u308a\u3001\u4e57\u7b97\u306e\u53ef\u63db\u6027\u3092\u7528\u3044\u3066\u5c0e\u304f}\\\\\n\n(7) &amp; \\bot &amp;\\text{\uff1b$(1)$ \u3068 $(6)$ \u306e\u77db\u76fe}\n\n\\end{array}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u3088\u3046\u306a\u7d50\u8ad6\u306b\u81f3\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{1 \\neq 1^\\prime, 1a= a, 1b = b\\}\\vdash \\bot.<\/span><\/span><\/p>\n<p>\u3088\u3063\u3066\u3001\u80cc\u7406\u6cd5\u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{1a= a, 1b= b\\}\\vdash 1 = 1^\\prime.<\/span><\/span><\/p>\n<p>\u3064\u307e\u308a\u3001\u3082\u3057\u4e57\u6cd5\u5358\u4f4d\u5143\u304c2\u3064\u5b58\u5728\u3059\u308b\u306a\u3089\u3001\u305d\u308c\u3089\u306f\u7b49\u3057\u304f\u3001\u3057\u305f\u304c\u3063\u3066\u4e00\u610f\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n<h4>\u52a0\u7b97\u306b\u5bfe\u3059\u308b\u7d04\u7c21\u6cd5\u5247\u304c\u6210\u308a\u7acb\u3064<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=461s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3053\u308c\u306f\u7b49\u5f0f\u306e\u4e2d\u306e\u9805\u3092\u524a\u9664\u3059\u308b\u969b\u306b\u884c\u3063\u3066\u3044\u308b\u3053\u3068\u3067\u3059\uff1a<\/span><\/strong><\/a><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b = a+c \\longleftrightarrow a = c<\/span><\/span><\/p>\n<p>\u3053\u306e\u72b6\u6cc1\u3092\u8a3c\u660e\u3059\u308b\u306e\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u6b21\u306e\u3088\u3046\u306a\u63a8\u8ad6\u3092\u884c\u3048\u3070\u3088\u3044\u306e\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a+b = a+c &amp; \\text{\uff1b\u524d\u63d0} \\\\\n\n(2) &amp; a+b-a = a+c-a &amp; \\text{\uff1b$(1)$ \u306b $-a$ \u3092\u4e21\u8fba\u306b\u52a0\u3048\u308b} \\\\\n\n(3) &amp; (a-a)+b = (a-a)+c &amp; \\text{\uff1b$(2)$ \u306b\u53ef\u63db\u6027\u3068\u7d50\u5408\u6027\u3092\u9069\u7528} \\\\\n\n(4) &amp; 0+b = 0+c &amp; \\text{\uff1b$(3)$ \u3088\u308a\u3001\u52a0\u6cd5\u9006\u5143\u3092\u7528\u3044\u308b} \\\\\n\n(5) &amp; b = c &amp; \\text{\uff1b$(4)$ \u3088\u308a\u3001\u52a0\u6cd5\u5358\u4f4d\u5143\u3092\u9069\u7528} \\\\\n\n\\end{array}<\/span>\n<p>\u3053\u306e\u63a8\u8ad6\u306f\u3001\u540c\u3058\u624b\u9806\u3092\u9006\u306b\u305f\u3069\u308b\u3053\u3068\u3067\u9006\u65b9\u5411\u306b\u3082\u6210\u308a\u7acb\u3064\u305f\u3081\u3001\u6b21\u306e\u3053\u3068\u304c\u8a00\u3048\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b=a+c \\dashv \\vdash b=c<\/span><\/span><\/p>\n<p>\u3053\u308c\u306f\u3001\u6b21\u306e\u547d\u984c\u3068\u540c\u5024\u3067\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash a+b=a+c \\longleftrightarrow b=c<\/span><\/span><\/p>\n<h4>\u52a0\u6cd5\u5358\u4f4d\u5143\u306f\u307e\u305f\u3001\u4e57\u6cd5\u306e\u5438\u53ce\u5143\u3067\u3082\u3042\u308b<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=632s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3053\u308c\u306f\u5358\u306b<\/span><\/strong><\/a>\u6574\u57df\u306b\u5c5e\u3059\u308b\u4efb\u610f\u306e <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u306b\u5bfe\u3057\u3066\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\cdot 0 = 0<\/span><\/span><\/p>\n<p>\u3053\u308c\u3082\u7c21\u5358\u306b\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u63a8\u8ad6\u306b\u5f93\u3048\u3070\u5341\u5206\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a\\cdot a + a\\cdot 0 = a\\cdot  (a+0) &amp; \\text{\uff1b\u5206\u914d\u6cd5\u5247}\\\\\n\n(2) &amp; a\\cdot a + a\\cdot 0 = a\\cdot  (a+a-a) &amp; \\text{\uff1b$(1)$ \u3068\u52a0\u6cd5\u9006\u5143\u3088\u308a}\\\\\n\n(3) &amp; a\\cdot a + a\\cdot 0 = a\\cdot a + a\\cdot a - a\\cdot a &amp; \\text{\uff1b$(2)$ \u3068\u5206\u914d\u6cd5\u5247\u3088\u308a}\\\\\n\n(4) &amp;  a\\cdot 0 =  a\\cdot a - a\\cdot a &amp; \\text{\uff1b$(3)$ \u3068\u52a0\u7b97\u306e\u7c21\u7d04\u6cd5\u5247\u3088\u308a}\\\\\n\n(5) &amp;  a\\cdot 0 =  0 &amp; \\text{\uff1b$(4)$ \u3068\u52a0\u6cd5\u9006\u5143\u3088\u308a}\\\\\n\n\\end{array}<\/span>\n<h4><strong>\u7b26\u53f7\u306e\u6cd5\u5247\uff1a<\/strong><\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=736s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u540c\u7b26\u53f7\u306e\u6570\u306e\u7a4d\u306f\u5e38\u306b\u6b63\u3067\u3042\u308a\u3001<\/span><\/strong><\/a>\u7570\u7b26\u53f7\u306e\u6570\u306e\u7a4d\u306f\u5e38\u306b\u8ca0\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u6027\u8cea\u306e\u8a3c\u660e\u3082\u7c21\u5358\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a\\cdot b = a\\cdot b + 0 &amp; \\text{\uff1b\u52a0\u6cd5\u5358\u4f4d\u5143}\\\\\n\n(2) &amp; a\\cdot b = a\\cdot b + (a)\\cdot(-b) - (a)\\cdot(-b) &amp; \\text{\uff1b$(1)$ \u3068\u52a0\u6cd5\u9006\u5143\u3088\u308a}\\\\\n\n(3) &amp; a\\cdot b = a\\cdot (b -b) - (a)\\cdot(-b) &amp; \\text{\uff1b$(2)$ \u3068\u52a0\u6cd5\u9006\u5143\u3088\u308a}\\\\\n\n(4) &amp; a\\cdot b = a\\cdot 0 + (-a)\\cdot(-b) &amp; \\text{\uff1b$(3)$ \u3068\u52a0\u6cd5\u9006\u5143\u3088\u308a}\\\\\n\n(5) &amp; a\\cdot b = (-a)\\cdot(-b) &amp; \\text{\uff1b$(4)$ \u3068\u4e57\u6cd5\u306e\u5438\u53ce\u6027\u3088\u308a}\\\\\n\n\\end{array}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\uff1a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> ab = (-a)(-b)<\/span><\/span><\/p>\n<p>\u7570\u7b26\u53f7\u306e\u5834\u5408\u3082\u540c\u69d8\u306b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a\\cdot(-b) = a \\cdot (-b) + 0 &amp; \\text{\uff1b\u52a0\u6cd5\u5358\u4f4d\u5143} \\\\\n\n(2) &amp; a\\cdot(-b) = a \\cdot (-b) + a \\cdot b  -  a \\cdot b  &amp; \\text{\uff1b$(1)$ \u3068\u52a0\u6cd5\u9006\u5143\u3088\u308a} \\\\\n\n(3) &amp; a\\cdot(-b) = a \\cdot (b-b)  -  a \\cdot b  &amp; \\text{\uff1b$(2)$ \u3068\u5206\u914d\u6cd5\u5247\u3088\u308a} \\\\\n\n(4) &amp; a\\cdot(-b) = a \\cdot 0  -  a \\cdot b  &amp; \\text{\uff1b$(3)$ \u3068\u52a0\u6cd5\u9006\u5143\u3088\u308a} \\\\\n\n(5) &amp; a\\cdot(-b) = - a \\cdot b  &amp; \\text{\uff1b$(4)$ \u3068\u4e57\u6cd5\u306e\u5438\u53ce\u6027\u3088\u308a} \\\\\n\n\\end{array}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\uff1a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(-b) = -a(b)<\/span><\/span><\/p>\n<h4>2\u3064\u306e\u6570\u306e\u7a4d\u304c0\u306a\u3089\u3070\u3001\u5c11\u306a\u304f\u3068\u3082\u4e00\u65b9\u306f0\u3067\u3042\u308b<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=875s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3053\u306e\u6027\u8cea\u3082\u307e\u305f<\/span><\/strong><\/a>\u975e\u5e38\u306b\u3088\u304f\u4f7f\u308f\u308c\u308b\u3082\u306e\u3067\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ab=0 \\leftrightarrow (a=0 \\vee b=0)<\/span><\/span><\/p>\n<p>\u3053\u306e\u8a3c\u660e\u3082\u7c21\u5358\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; \\{a=0\\} \\models a\\cdot b = 0  &amp; \\textbf{\uff1b\u4e57\u6cd5\u306e\u5438\u53ce\u6027} \\\\\n\n(2) &amp; \\models a=0 \\rightarrow a\\cdot b = 0  &amp;\\text{\uff1bTD$(1)$} \\\\\n\n(3) &amp; \\models \\neg (a\\cdot b = 0 ) \\rightarrow \\neg(a=0) &amp;\\text{\uff1bCPI$(2)$} \\\\\n\n(4) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models   \\neg(a=0) &amp;\\text{\uff1bRTD$(3)$} \\\\\n\n(5) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models   \\neg(b=0) &amp;\\text{\uff1b\u540c\u69d8\u306b$(4)$\u3088\u308a} \\\\\n\n(6) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models  \\neg(a=0) \\wedge \\neg(b=0) &amp;\\text{\uff1b$\\wedge$-\u5c0e\u5165$(4,5)$} \\\\\n\n(7) &amp; \\models (\\neg (a\\cdot b = 0 )) \\rightarrow \\neg(a=0) \\wedge \\neg(b=0)  &amp;\\text{\uff1bTD(6)} \\\\\n\n(8) &amp; \\models \\neg(\\neg(a=0) \\wedge \\neg(b=0) ) \\rightarrow   (a\\cdot b = 0 ) &amp;\\text{\uff1bCPI(7)} \\\\\n\n(9) &amp; \\models (a=0 \\vee b=0) \\rightarrow   (a\\cdot b = 0 ) &amp;\\text{\uff1b\u30c9\u30fb\u30e2\u30eb\u30ac\u30f3(8)} \\\\\n\n(10)&amp; \\{a\\neq 0 , a\\cdot b=0\\} \\models b=0 &amp; \\textbf{\uff1b\u4e57\u6cd5\u306e\u5438\u53ce\u6027} \\\\\n\n(11)&amp; \\{a\\cdot b=0\\} \\models a\\neq 0 \\rightarrow  b=0 &amp; \\text{\uff1bTD(10)} \\\\\n\n(12)&amp; \\{a\\cdot b=0\\} \\models \\neg(a\\neq 0) \\vee  b=0 &amp; \\text{\uff1b$\\rightarrow$\u306e\u5b9a\u7fa9(11)} \\\\\n\n(13)&amp; \\{a\\cdot b=0\\} \\models a=0 \\vee  b=0 &amp; \\text{\uff1b\u4e8c\u91cd\u5426\u5b9a(12)} \\\\\n\n(14)&amp; \\models (a\\cdot b=0) \\rightarrow (a=0 \\vee  b=0) &amp; \\text{\uff1bTD(13)} \\\\\n\n(15)&amp; \\models (a\\cdot b=0) \\leftrightarrow (a=0 \\vee  b=0) &amp; \\text{\uff1b$(9)$ \u3068 $(14)$ \u3088\u308a}\n\n\\end{array}<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KZQ3PXeMlKk?si=O_Hek5KFG853Q6qT\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u7df4\u7fd2\u554f\u984c<\/h2>\n<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> \u3092\u6574\u57df <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u306e\u4efb\u610f\u306e\u8981\u7d20\u3068\u3059\u308b\u3002\u4ee5\u4e0b\u306e\u6027\u8cea\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u305b\u3088\uff1a<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(-a)=(-1)a<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=306s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3010\u89e3\u8aac\u3011<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-(a+b)=(-a) + (-b)<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=827s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3010\u89e3\u8aac\u3011<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(-b)=-(ab)<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=1213s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3010\u89e3\u8aac\u3011<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-(-a)=a<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=1628s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3010\u89e3\u8aac\u3011<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(b-c) = ab - ac<\/span><\/span> <strong>\u3010\u6f14\u7fd2\u3011<\/strong><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a-b)+(b-c) = a-c<\/span><\/span> <strong>\u3010\u6f14\u7fd2\u3011<\/strong><\/li>\n<li>\u4efb\u610f\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\in D<\/span><\/span> \u306b\u5bfe\u3057\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\cdot 1 = a<\/span><\/span> \u3092\u6e80\u305f\u3059\u4e00\u610f\u306a <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u304c\u5b58\u5728\u3059\u308b\u3002<a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=2029s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3010\u89e3\u8aac\u3011<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">xx = x \\leftrightarrow (x=1 \\vee x=0)<\/span><\/span> <strong>\u3010\u6f14\u7fd2\u3011<\/strong><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6574\u57df\u3068\u6574\u6570 \u8981\u7d04\uff1a \u672c\u8b1b\u7fa9\u3067\u306f\u3001\u6574\u57df\u306e\u6982\u5ff5\u3092\u5c0e\u5165\u3057\u3001\u305d\u308c\u304c\u4e00\u822c\u4ee3\u6570\u5b66\u306e\u7814\u7a76\u306b\u304a\u3044\u3066\u3044\u304b\u306b\u91cd\u8981\u3067\u3042\u308b\u304b\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u5f62\u5f0f\u7684\u8a3c\u660e\u3092\u901a\u3058\u3066\u3001\u305d\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u306e\u3044\u304f\u3064\u304b\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\u3002 h \u5b66\u7fd2\u76ee\u6a19\uff1a \u672c\u8b1b\u7fa9\u3092\u4fee\u4e86\u3057\u305f\u5b66\u751f\u306f\u4ee5\u4e0b\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a \u7406\u89e3\u3059\u308b\uff1a\u4e00\u822c\u4ee3\u6570\u5b66\u306e\u7814\u7a76\u76ee\u7684\u3092\u7406\u89e3\u3059\u308b\u3002 \u7406\u89e3\u3059\u308b\uff1a\u6574\u57df\u306e\u6982\u5ff5\u3092\u7406\u89e3\u3059\u308b\u3002 \u8aac\u660e\u3059\u308b\uff1a\u6574\u57df\u3068\u6574\u6570\u306b\u5171\u901a\u3059\u308b\u57fa\u672c\u7684\u5074\u9762\u3092\u8aac\u660e\u3059\u308b\u3002 \u8a3c\u660e\u3059\u308b\uff1a\u6574\u57df\u306e\u57fa\u672c\u7684\u6027\u8cea\u3092\u5f62\u5f0f\u7684\u8a3c\u660e\u306b\u3088\u3063\u3066\u793a\u3059\u3002 \u76ee\u6b21 \u4e00\u822c\u4ee3\u6570\u5b66\u306e\u76ee\u7684\u3068\u4e88\u5099\u77e5\u8b58 \u6574\u6570\u304b\u3089\u6574\u57df\u3078 \u6574\u57df\u3068\u6574\u6570\u306b\u5171\u901a\u3059\u308b\u57fa\u672c\u7684\u5074\u9762 \u6574\u57df\u3068\u6574\u6570\u306e\u6027\u8cea \u7df4\u7fd2\u554f\u984c \u4e00\u822c\u4ee3\u6570\u5b66\u306e\u76ee\u7684\u3068\u4e88\u5099\u77e5\u8b58 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