{"id":28260,"date":"2021-04-09T13:00:50","date_gmt":"2021-04-09T13:00:50","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28260"},"modified":"2024-09-03T21:31:50","modified_gmt":"2024-09-03T21:31:50","slug":"%e0%a4%87%e0%a4%82%e0%a4%a1%e0%a4%95%e0%a5%8d%e0%a4%b6%e0%a4%a8-%e0%a4%a6%e0%a5%8d%e0%a4%b5%e0%a4%be%e0%a4%b0%e0%a4%be-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%ae%e0%a4%be%e0%a4%a3-%e0%a4%a1%e0%a5%80","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%87%e0%a4%82%e0%a4%a1%e0%a4%95%e0%a5%8d%e0%a4%b6%e0%a4%a8-%e0%a4%a6%e0%a5%8d%e0%a4%b5%e0%a4%be%e0%a4%b0%e0%a4%be-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%ae%e0%a4%be%e0%a4%a3-%e0%a4%a1%e0%a5%80\/","title":{"rendered":"\u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923: \u0921\u0940 \u092e\u0949\u0930\u094d\u0917\u0928 \u0914\u0930 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923: \u0921\u0940 \u092e\u0949\u0930\u094d\u0917\u0928 \u0914\u0930 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0928\u093f\u092f\u092e<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0938\u093e\u0930\u093e\u0902\u0936<\/strong><br \/><em>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0917\u0923\u093f\u0924 \u0914\u0930 \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u092e\u0947\u0902 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u0947 \u0935\u093f\u0937\u092f \u0915\u094b \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0926\u094b 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\u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0910\u0938\u0947 \u092a\u094d\u0930\u092e\u093e\u0923\u094b\u0902 \u0915\u094b \u00ab\u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0915\u0947 \u092d\u0940\u0924\u0930\u00bb \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0907\u0938\u0932\u093f\u090f \u0907\u0928\u094d\u0939\u0947\u0902 \u00ab\u0906\u0902\u0924\u0930\u093f\u0915\u00bb \u092f\u093e \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u092a\u094d\u0930\u092e\u093e\u0923 \u092d\u0940 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u094d\u0930\u092e\u093e\u0923\u094b\u0902 \u0915\u093e \u090f\u0915 \u0938\u0940\u092e\u093f\u0924 \u0926\u093e\u092f\u0930\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u0947 \u0915\u0947\u0935\u0932 \u0909\u0928 \u0915\u0925\u0928\u094b\u0902 \u0915\u094b \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093e\u092e \u0906\u0924\u0947 \u0939\u0948\u0902 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0915\u0940 \u092d\u093e\u0937\u093e \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u0939\u092e \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0915\u0941\u091b \u092c\u093e\u0924\u0947\u0902 \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u092e \u092f\u0939 \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0915\u0947 \u0938\u092d\u0940 \u0915\u0925\u0928 \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u0917\u0941\u0923 \u0915\u0947 \u0938\u093e\u0925 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0910\u0938\u0947 \u0915\u0925\u0928 \u091c\u094b \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0938\u094d\u0935\u092f\u0902 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0909\u0928\u094d\u0939\u0947\u0902 \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0928 \u0924\u094b \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u0928 \u0939\u0940 \u0938\u093e\u092c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0910\u0938\u0947 \u0915\u0925\u0928\u094b\u0902 \u0915\u094b \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u090f\u0915 \u092c\u093e\u0939\u0930\u0940 \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092c\u093e\u0939\u0930\u0940 \u092a\u094d\u0930\u092e\u093e\u0923\u094b\u0902 \u0915\u094b \u0915\u092d\u0940-\u0915\u092d\u0940 \u00ab\u092e\u0947\u091f\u093e\u092e\u0948\u0925\u0947\u092e\u0947\u091f\u093f\u0915\u0932\u00bb \u092d\u0940 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0939\u092e \u092a\u0939\u0932\u0947 \u092d\u0940 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u091a\u0940\u091c\u094b\u0902 \u0915\u093e \u0938\u093e\u092e\u0928\u093e \u0915\u0930 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902, \u091c\u0948\u0938\u0947 \u0915\u093f \u091c\u092c \u0939\u092e\u0928\u0947 (\u092e\u0947\u091f\u093e)\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0926\u0947\u0916\u093e \u0925\u093e\u0964 \u092f\u0939\u0940 \u0935\u0939 \u0938\u0902\u0926\u0930\u094d\u092d \u0939\u0948 \u091c\u0939\u093e\u0901 \u0939\u092e \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0947 \u092a\u094d\u0930\u092e\u093e\u0923\u094b\u0902 \u0915\u094b \u0938\u092e\u091d\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0917\u0923\u093f\u0924\u0940\u092f \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=eJQcNPrKyW0&amp;t=359s\" target=\"_blank\" rel=\"noopener\"><strong>\u0917\u0923\u093f\u0924\u0940\u092f \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u090f\u0915 \u092a\u094d\u0930\u092e\u093e\u0923\u0940\u0915\u0930\u0923 \u0935\u093f\u0927\u093f \u0939\u0948<\/strong><\/a> \u091c\u094b \u0939\u092e\u0947\u0902 \u092f\u0939 \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0940 \u0939\u0948 \u0915\u093f \u0915\u0941\u091b \u092c\u093e\u0924\u0947\u0902 \u0938\u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u094d\u092f \u0939\u0948\u0902\u0964<\/p>\n<p style=\"text-align: justify;\"><strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><br \/>\n\u0910\u0938\u0947 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948 \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11^n - 4^n<\/span><\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0915\u094b\u0908 \u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b, \u0939\u092e\u0947\u0936\u093e 7 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br \/>\n<strong>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong> \u092f\u0926\u093f \u0939\u092e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=1<\/span><\/span> \u0915\u0947 \u0938\u093e\u0925 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11^1 - 4^1 = 7<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u091c\u094b \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947, 7 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0905\u092c \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11^n - 4^n<\/span><\/span> \u0915\u093f\u0938\u0940 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=k<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 \u0939\u092e \u092f\u0939 \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u092f\u0939 \u0915\u0925\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=k+1<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u094b\u0917\u093e\u0964 \u0907\u0938\u0947 \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<table\">\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11^{k+1} - 4^{k+1}<\/span><\/span><\/td>\n<td style=\"text-align: left;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">=11 \\cdot 11^{k} - 4 \\cdot 4^{k}<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><\/td>\n<td style=\"text-align: left;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">=11 \\cdot 11^{k} - (11-7) \\cdot 4^{k}<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><\/td>\n<td style=\"text-align: left;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">=11 \\cdot 11^{k} - 11 \\cdot 4^{k} + 7\\cdot 4^{k}<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><\/td>\n<td style=\"text-align: left;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">=11 ( 11^{k} - 4^{k} ) + 7\\cdot 4^{k}<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0907\u0938\u0932\u093f\u090f, \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11^k - 4^k<\/span><\/span> 7 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11 ( 11^{k} - 4^{k} ) + 7\\cdot 4^{k}<\/span><\/span> \u092d\u0940 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u094b\u0917\u093e, \u091c\u094b \u092f\u0939 \u0915\u0939\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11^{k+1} - 4^{k+1}<\/span><\/span> 7 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948\u0964 \u092f\u0939\u093e\u0901 \u0938\u0947 \u0939\u092e \u091c\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11^k - 4^k<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=1<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948, \u0924\u094b \u092f\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=2, k=3, k=4,\\cdots<\/span><\/span> \u0914\u0930 \u0907\u0938\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u094b\u0917\u093e, \u0914\u0930 \u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0915\u093f\u0938\u0940 \u092d\u0940 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\in\\mathbb{N}.<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u094b\u0917\u093e\u0964 \u091c\u092c \u0910\u0938\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u0924\u094b \u0939\u092e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u25a0<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0924\u0930\u094d\u0915 \u092e\u0947\u0902 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=eJQcNPrKyW0&amp;t=775s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u093f\u0928 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923\u094b\u0902 \u0915\u094b \u0939\u092e \u0906\u0917\u0947 \u0915\u0930\u0947\u0902\u0917\u0947,<\/strong><\/a> \u0909\u0928\u0915\u0947 \u0932\u093f\u090f \u092a\u0939\u0932\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0928\u094b\u091f\u0947\u0936\u0928 \u0938\u092e\u091d\u094c\u0924\u0947 \u0915\u094b \u092a\u0947\u0936 \u0915\u0930\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b\u0917\u093e\u0964<\/p>\n<p style=\"text-align: justify;\"><strong>\u0928\u094b\u091f\u0947\u0936\u0928:<\/strong> \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1,\\cdots, F_n<\/span><\/span> \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0924\u0930\u094d\u0915 \u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0905\u0938\u0940\u092e\u093f\u0924 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u090f\u0915 \u0938\u0947\u091f \u0939\u0948\u0964 \u0907\u0928 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u0902\u092f\u094b\u091c\u0928\u094b\u0902 \u0914\u0930 \u0935\u093f\u0938\u094d\u0925\u093e\u092a\u0928\u093e\u0913\u0902 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigwedge_{i=1}^n F_i := F_1\\wedge \\cdots \\wedge F_n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigvee_{i=1}^n F_i := F_1\\vee \\cdots \\vee F_n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938\u0915\u0947 \u0938\u093e\u0925 \u0939\u092e \u0905\u092c \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0926\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0930\u0942\u092a\u094b\u0902 \u0915\u093e \u0938\u093e\u092e\u0928\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0921\u0940 \u092e\u0949\u0930\u094d\u0917\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0930\u0942\u092a<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=eJQcNPrKyW0&amp;t=829s\" target=\"_blank\" rel=\"noopener\"><strong>\u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0915\u0947 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0924\u0930\u094d\u0915 \u092e\u0947\u0902 \u090f\u0915 \u0938\u0940\u092e\u093f\u0924 \u0938\u0947\u091f \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1,\\cdots, F_n,<\/span><\/span> \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0926\u094b \u0917\u0941\u0923 \u0939\u092e\u0947\u0936\u093e \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\neg\\left(\\bigwedge_{i=1}^n F_i \\right) \\equiv \\left( \\bigvee_{i=1}^n \\neg F_i \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\neg\\left(\\bigvee_{i=1}^n F_i \\right) \\equiv \\left( \\bigwedge_{i=1}^n \\neg F_i \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><strong>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong> \u092a\u0939\u0932\u0947 \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u092a\u0930 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg\\left(\\bigwedge_{i=1}^n F_i \\right) \\equiv \\left( \\bigvee_{i=1}^n \\neg F_i \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u092a\u0939\u0932\u0947 \u0939\u092e\u0947\u0902 \u0926\u0947\u0916\u0928\u093e \u0939\u094b\u0917\u093e \u0915\u093f \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092e\u093e\u092e\u0932\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=1.<\/span><\/span> \u0915\u0947 \u0938\u093e\u0925 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902, \u092f\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg F_1 \\equiv \\neg\\left(\\bigwedge_{i=1}^1F_i\\right)\\equiv \\left(\\bigvee_{i=1}^n \\neg F_i \\right) \\equiv\\neg F_1<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0905\u092c \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u092f\u0939 \u0917\u0941\u0923 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=k;<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0915\u093e\u092e \u0915\u0930\u0924\u093e \u0939\u0948, \u092f\u093e\u0928\u0940 \u0915\u093f \u090f\u0915 \u0938\u0940\u092e\u093f\u0924 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1, F_2, \\cdots, F_k<\/span><\/span> \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u0924\u094b \u092f\u0939 \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\neg\\left(\\bigwedge_{i=1}^k F_i\\right) \\equiv \\left(\\bigvee_{i=1}^k \\neg F_i\\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify\">\u092b\u093f\u0930 \u0939\u092e \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u092f\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\neg\\left(\\bigwedge_{i=1}^{k+1} F_i\\right) \\equiv \\left(\\bigvee_{i=1}^{k+1} \\neg F_i\\right)<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0938\u0939\u0940 \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify\">\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f:<\/p>\n<p style=\"text-align: justify\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\neg\\left(\\bigwedge_{i=1}^{k+1} F_i\\right) := \\neg\\left[\\left(\\bigwedge_{i=1}^{k} F_i\\right) \\wedge F_{k+1}\\right]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u092a\u0930 \u0939\u092e \u0921\u0940 \u092e\u0949\u0930\u094d\u0917\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 (\u0926\u094b \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0928\u093f\u092f\u092e) \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\neg\\left(\\bigwedge_{i=1}^{k+1} F_i\\right)\\equiv \\left[\\neg\\left(\\bigwedge_{i=1}^{k} F_i\\right) \\vee \\neg F_{k+1}\\right]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0905\u092c, \u092f\u0926\u093f \u0939\u092e \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0940 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u092a\u093e\u090f\u0902\u0917\u0947:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\neg\\left(\\bigwedge_{i=1}^{k+1} F_i\\right)\\equiv \\left[ \\left(\\bigvee_{i=1}^k \\neg F_i\\right) \\vee \\neg F_{k+1}\\right] := \\left(\\bigvee_{i=1}^{k+1}\\neg F_i \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0914\u0930 \u0907\u0938 \u0915\u093e\u0930\u0923 \u0938\u0947 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u092a\u0942\u0930\u094d\u0923 \u0939\u0948 \u0914\u0930 \u0917\u0941\u0923 \u0938\u092d\u0940 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u093e \u0938\u0902\u092c\u0902\u0927 \u0938\u092e\u093e\u0928 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092e\u0948\u0902 \u0907\u0938\u0947 \u092a\u093e\u0920\u0915 \u0915\u0947 \u0932\u093f\u090f \u091b\u094b\u0921\u093c \u0926\u0942\u0901\u0917\u093e \u0939\u093e \u0939\u093e!<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0930\u0942\u092a<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=eJQcNPrKyW0&amp;t=1205s\" target=\"_blank\" rel=\"noopener\"><strong>\u0921\u0940 \u092e\u0949\u0930\u094d\u0917\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u0947 \u0938\u092e\u093e\u0928<\/strong><\/a>, \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{F_1, \\cdots, F_n\\}<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{G_1,\\cdots, G_m\\}<\/span><\/span> \u0915\u094b\u0908 \u092d\u0940 \u0926\u094b \u0938\u0940\u092e\u093f\u0924 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u092e\u0942\u0939 \u0939\u0948\u0902, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u093e\u0928\u0924\u093e\u090f\u0901 \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u0940 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^m G_j \\right) \\right] \\equiv \\left[\\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^m(F_i\\vee G_j) \\right) \\right]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigvee_{i=1}^n F_i \\right) \\wedge \\left(\\bigvee_{j=1}^m G_j \\right) \\right] \\equiv \\left[\\bigvee_{i=1}^n\\left(\\bigvee_{j=1}^m(F_i\\wedge G_j) \\right) \\right]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><strong>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong> \u0907\u0938 \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u094b \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> \u092a\u0930 \u0921\u092c\u0932 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0930\u0928\u093e \u0939\u094b\u0917\u093e\u0964 \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947 \u092e\u0948\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u092a\u0930 \u0914\u0930 \u092b\u093f\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> \u092a\u0930 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0930\u0942\u0901\u0917\u093e, \u0924\u093e\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^m G_j \\right) \\right] \\equiv \\left[\\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^m(F_i\\vee G_j) \\right) \\right]<\/span><\/span> \u0915\u0940 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964<\/p>\n<p style=\"text-align: justify;\">\u092f\u0926\u093f \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=1,<\/span><\/span> \u0932\u0947\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092f\u0939 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0932\u093f\u0916\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^1 G_j \\right) \\right] \\equiv \\left[\\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^1(F_i\\vee G_j) \\right) \\right].<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u091c\u093f\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u092f\u0939\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee G_1 \\right] \\equiv \\left[\\bigwedge_{i=1}^n\\left( F_i\\vee G_1 \\right) \\right].<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0905\u092c \u0939\u092e \u0907\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n.<\/span><\/span> \u092a\u0930 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0917\u0947:<\/p>\n<p style=\"text-align: justify;\">\u092f\u0926\u093f \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=1,<\/span><\/span> \u0932\u0947\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092f\u0939 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1 \\vee G_1 \\equiv F_1 \\vee G_1.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u091c\u094b \u0915\u093f \u0938\u0924\u094d\u092f \u0939\u0948\u0964 \u0905\u092c \u092e\u093e\u0928 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092f\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=k<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u094d\u092f \u0939\u0948; \u0905\u0930\u094d\u0925\u093e\u0924, \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0940 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092f\u0939 \u0939\u094b\u0917\u0940:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^k F_i \\right) \\vee G_1 \\right] \\equiv \\left[\\bigwedge_{i=1}^k\\left( F_i\\vee G_1 \\right) \\right].<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938\u0938\u0947 \u0939\u092e \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u092f\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n=k+1.<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[\\left(\\bigwedge_{i=1}^{k+1}F_i \\right) \\vee G_1 \\right] := \\left[\\left(\\left(\\bigwedge_{i=1}^{k}F_i \\right)\\wedge F_{k+1} \\right) \\vee G_1 \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0905\u092c, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[\\left(\\bigwedge_{i=1}^{k+1}F_i \\right) \\vee G_1 \\right] \\equiv \\left[\\left(\\left(\\bigwedge_{i=1}^{k}F_i \\right)\\vee G_{1} \\right) \\wedge \\left(F_{k+1} \\vee G_1 \\right) \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0914\u0930 \u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u0939\u092e \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0940 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[\\left(\\bigwedge_{i=1}^{k+1}F_i \\right) \\vee G_1 \\right] \\equiv \\left[\\left(\\bigwedge_{i=1}^k\\left( F_i\\vee G_1 \\right) \\right) \\wedge \\left(F_{k+1} \\vee G_1 \\right) \\right] := \\left[\\bigwedge_{i=1}^{k+1}(F_{i}\\vee G_1 \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938\u0932\u093f\u090f, \u0939\u092e\u0928\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930 \u0926\u093f\u092f\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\in\\mathbb{N}<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0938\u0924\u094d\u092f \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right)\\vee G_1\\right] \\equiv \\left[\\bigwedge_{i=1}^n(F_i\\vee G_1)\\right]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u092a\u0930 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e\u0928\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u0915\u093f \u092f\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=1,<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0924\u093e \u0939\u0948, \u0914\u0930 \u0905\u092c \u0939\u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> \u092a\u0930 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u093e \u0939\u0948\u0964 \u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=l<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0940 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0905\u0930\u094d\u0925\u093e\u0924:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^l G_j \\right) \\right] \\equiv \\left[\\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^l(F_i\\vee G_j) \\right) \\right]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0914\u0930 \u0907\u0938\u0938\u0947 \u0939\u092e \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u092f\u0939 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=l+1.<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^{l+1} G_j \\right) \\right] := \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\left(\\bigwedge_{j=1}^{l} G_j \\right) \\wedge G_{l+1}\\right) \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0905\u092c, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^{l+1} G_j \\right) \\right] \\equiv \\left[ \\left( \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left( \\bigwedge_{j=1}^l G_j \\right) \\right) \\wedge \\left( \\left( \\bigwedge_{i=1}^n F_i \\right)\\vee G_{l+1} \\right) \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938\u0932\u093f\u090f, \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0940 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^{l+1} G_j \\right) \\right] \\equiv \\left[ \\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^l(F_i\\vee G_j) \\right) \\wedge \\left( \\left( \\bigwedge_{i=1}^n F_i \\right)\\vee G_{l+1} \\right) \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0905\u092c \u092f\u0926\u093f \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u092a\u0930 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u0932\u0947\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^{l+1} G_j \\right) \\right] \\equiv \\left[ \\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^l(F_i\\vee G_j) \\right) \\wedge \\left( \\bigwedge_{i=1}^n (F_i \\vee G_{l+1} )\\right) \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0905\u0902\u0924 \u092e\u0947\u0902, \u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^{l+1} G_j \\right) \\right] \\equiv \\left[ \\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^{l+1}(F_i\\vee G_j) \\right) \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> \u092a\u0930 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u092a\u0942\u0930\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u0914\u0930 \u092f\u0939 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[ \\left(\\bigwedge_{i=1}^n F_i \\right) \\vee \\left(\\bigwedge_{j=1}^{m} G_j \\right) \\right] \\equiv \\left[ \\bigwedge_{i=1}^n\\left(\\bigwedge_{j=1}^{m}(F_i\\vee G_j) \\right) \\right] <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n,m\\in\\mathbb{N}<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f\u0964<\/p>\n<p style=\"text-align: justify;\">\u092f\u0939 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u0948\u0938\u0947 \u0915\u0920\u094b\u0930 \u0917\u0923\u093f\u0924\u0940\u092f \u092a\u094d\u0930\u092e\u093e\u0923 \u0924\u0915\u0928\u0940\u0915\u0947\u0902 \u0928 \u0915\u0947\u0935\u0932 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092e\u0947\u0902 \u092c\u0932\u094d\u0915\u093f \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u092e\u0947\u0902 \u092d\u0940 \u0932\u093e\u0917\u0942 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964 \u0907\u0902\u0921\u0915\u094d\u0936\u0928 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0939\u092e\u0928\u0947 \u0921\u0940 \u092e\u0949\u0930\u094d\u0917\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0914\u0930 \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0930\u0942\u092a\u094b\u0902 \u0915\u0940 \u0938\u0924\u094d\u092f\u0924\u093e \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0940 \u0939\u0948, \u091c\u094b \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0917\u0923\u093f\u0924\u0940\u092f \u091c\u094d\u091e\u093e\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0928\u0940\u0902\u0935\u094b\u0902 \u0915\u0940 \u0938\u092e\u091d \u0915\u094b \u092e\u091c\u092c\u0942\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0928 \u0915\u0947\u0935\u0932 \u0905\u092e\u0942\u0930\u094d\u0924 \u0938\u094b\u091a 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