{"id":3087,"date":"2025-06-07T09:57:19","date_gmt":"2025-06-07T09:57:19","guid":{"rendered":"https:\/\/diznr.com\/?p=3087"},"modified":"2025-06-07T09:57:19","modified_gmt":"2025-06-07T09:57:19","slug":"part-07-discrete-mathematics-for-gate-example-based-on-symmetry-anti-symmetry-asymmetry-and","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/part-07-discrete-mathematics-for-gate-example-based-on-symmetry-anti-symmetry-asymmetry-and\/","title":{"rendered":"Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry."},"content":{"rendered":"<p>Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry.<\/p>\n<p>[fvplayer id=&#8221;246&#8243;]<\/p>\n<h2 data-start=\"0\" data-end=\"100\"><strong data-start=\"3\" data-end=\"98\">Part 07 &#8211; Discrete Mathematics for GATE: Examples on Symmetry, Anti-Symmetry, and Asymmetry<\/strong><\/h2>\n<h3 data-start=\"102\" data-end=\"145\"><strong data-start=\"106\" data-end=\"145\">1. Symmetric Relation (\u0938\u092e\u092e\u093f\u0924 \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h3>\n<blockquote data-start=\"146\" data-end=\"209\">\n<p data-start=\"148\" data-end=\"209\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">(a,b)\u2208R(a, b) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0939\u0948, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">(b,a)\u2208R(b, a) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u092d\u0940 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<\/blockquote>\n<h4 data-start=\"211\" data-end=\"254\"><strong data-start=\"216\" data-end=\"252\">Example 1: &#8220;Friendship Relation&#8221;<\/strong><\/h4>\n<ul data-start=\"255\" data-end=\"445\">\n<li data-start=\"255\" data-end=\"334\">\u0905\u0917\u0930 <strong data-start=\"261\" data-end=\"268\">\u0930\u093e\u092e<\/strong> \u0914\u0930 <strong data-start=\"272\" data-end=\"281\">\u0936\u094d\u092f\u093e\u092e<\/strong> \u0926\u094b\u0938\u094d\u0924 \u0939\u0948\u0902, \u0924\u094b <strong data-start=\"296\" data-end=\"305\">\u0936\u094d\u092f\u093e\u092e<\/strong> \u0914\u0930 <strong data-start=\"309\" data-end=\"316\">\u0930\u093e\u092e<\/strong> \u092d\u0940 \u0926\u094b\u0938\u094d\u0924 \u0939\u094b\u0902\u0917\u0947\u0964<\/li>\n<li data-start=\"335\" data-end=\"407\">\u092f\u093e\u0928\u0940, \u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">(\u0930\u093e\u092e,\u0936\u094d\u092f\u093e\u092e)\u2208R(\u0930\u093e\u092e, \u0936\u094d\u092f\u093e\u092e) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord brahmic_fallback\">\u0930\u093e\u092e<\/span><span class=\"mpunct\">,<\/span><span class=\"mord brahmic_fallback\">\u0936\u094d\u092f\u093e\u092e<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span>, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">(\u0936\u094d\u092f\u093e\u092e,\u0930\u093e\u092e)\u2208R(\u0936\u094d\u092f\u093e\u092e, \u0930\u093e\u092e) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord brahmic_fallback\">\u0936\u094d\u092f\u093e\u092e<\/span><span class=\"mpunct\">,<\/span><span class=\"mord brahmic_fallback\">\u0930\u093e\u092e<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u092d\u0940 \u0939\u094b\u0917\u093e\u0964<\/li>\n<li data-start=\"408\" data-end=\"445\">\u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0938\u0902\u092c\u0902\u0927 <strong data-start=\"426\" data-end=\"442\">Symmetric \u0939\u0948<\/strong>\u0964<\/li>\n<\/ul>\n<h4 data-start=\"447\" data-end=\"494\"><strong data-start=\"452\" data-end=\"492\">Example 2: &#8220;Equality Relation ( = )&#8221;<\/strong><\/h4>\n<ul data-start=\"495\" data-end=\"625\">\n<li data-start=\"495\" data-end=\"535\">\u092f\u0926\u093f <strong data-start=\"501\" data-end=\"510\">a = b<\/strong>, \u0924\u094b <strong data-start=\"515\" data-end=\"524\">b = a<\/strong> \u092d\u0940 \u0939\u094b\u0917\u093e\u0964<\/li>\n<li data-start=\"536\" data-end=\"591\">\u092f\u093e\u0928\u0940, <span class=\"katex\"><span class=\"katex-mathml\">(a,b)\u2208R(a, b) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">(b,a)\u2208R(b, a) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u092d\u0940 \u0939\u094b\u0917\u093e\u0964<\/li>\n<li data-start=\"592\" data-end=\"625\">\u092f\u0939 \u0938\u0902\u092c\u0902\u0927 \u092d\u0940 <strong data-start=\"606\" data-end=\"622\">Symmetric \u0939\u0948<\/strong>\u0964<\/li>\n<\/ul>\n<h3 data-start=\"632\" data-end=\"685\"><strong data-start=\"636\" data-end=\"685\">2. Anti-Symmetric Relation (\u092a\u094d\u0930\u0924\u093f\u0938\u092e\u092e\u093f\u0924 \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h3>\n<blockquote data-start=\"686\" data-end=\"771\">\n<p data-start=\"688\" data-end=\"771\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">(a,b)\u2208R(a, b) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">(b,a)\u2208R(b, a) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0926\u094b\u0928\u094b\u0902 \u0938\u0924\u094d\u092f \u0939\u0948\u0902, \u0924\u094b <strong data-start=\"748\" data-end=\"757\">a = b<\/strong> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<\/blockquote>\n<h4 data-start=\"773\" data-end=\"816\"><strong data-start=\"778\" data-end=\"814\">Example 1: &#8220;Subset Relation (\u2286)&#8221;<\/strong><\/h4>\n<ul data-start=\"817\" data-end=\"1013\">\n<li data-start=\"817\" data-end=\"880\">\u092f\u0926\u093f <strong data-start=\"823\" data-end=\"832\">A \u2286 B<\/strong> \u0914\u0930 <strong data-start=\"836\" data-end=\"845\">B \u2286 A<\/strong>, \u0924\u094b \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c <strong data-start=\"860\" data-end=\"869\">A = B<\/strong> \u0939\u0940 \u0939\u094b\u0917\u093e\u0964<\/li>\n<li data-start=\"881\" data-end=\"970\">\u092f\u093e\u0928\u0940, <span class=\"katex\"><span class=\"katex-mathml\">(A,B)\u2208R(A, B) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">(B,A)\u2208R(B, A) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f <strong data-start=\"940\" data-end=\"967\">A \u0914\u0930 B \u0938\u092e\u093e\u0928 (equal) \u0939\u0948\u0902<\/strong>\u0964<\/li>\n<li data-start=\"971\" data-end=\"1013\">\u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0938\u0902\u092c\u0902\u0927 <strong data-start=\"989\" data-end=\"1007\">Anti-Symmetric<\/strong> \u0939\u0948\u0964<\/li>\n<\/ul>\n<h4 data-start=\"1015\" data-end=\"1064\"><strong data-start=\"1020\" data-end=\"1062\">Example 2: &#8220;Divisibility Relation (|)&#8221;<\/strong><\/h4>\n<ul data-start=\"1065\" data-end=\"1310\">\n<li data-start=\"1065\" data-end=\"1162\">\u092f\u0926\u093f <strong data-start=\"1071\" data-end=\"1080\">a | b<\/strong> (a, b \u0915\u094b \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948) \u0914\u0930 <strong data-start=\"1110\" data-end=\"1119\">b | a<\/strong> \u0926\u094b\u0928\u094b\u0902 \u0938\u0924\u094d\u092f \u0939\u0948\u0902, \u0924\u094b \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c a = b \u0939\u094b\u0917\u093e\u0964<\/li>\n<li data-start=\"1163\" data-end=\"1267\">\u0909\u0926\u093e\u0939\u0930\u0923: <strong data-start=\"1173\" data-end=\"1182\">4 | 4<\/strong> \u0914\u0930 <strong data-start=\"1186\" data-end=\"1195\">6 | 6<\/strong> \u0938\u0902\u092d\u0935 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 <strong data-start=\"1211\" data-end=\"1220\">4 | 2<\/strong> \u0914\u0930 <strong data-start=\"1224\" data-end=\"1233\">2 | 4<\/strong> \u0926\u094b\u0928\u094b\u0902 \u090f\u0915 \u0938\u093e\u0925 \u0938\u0924\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u0947\u0964<\/li>\n<li data-start=\"1268\" data-end=\"1310\">\u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0938\u0902\u092c\u0902\u0927 <strong data-start=\"1286\" data-end=\"1307\">Anti-Symmetric \u0939\u0948<\/strong>\u0964<\/li>\n<\/ul>\n<h3 data-start=\"1317\" data-end=\"1363\"><strong data-start=\"1321\" data-end=\"1363\">3. Asymmetric Relation (\u0905\u0938\u092e\u093e\u0928\u094d\u092f \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h3>\n<blockquote data-start=\"1364\" data-end=\"1427\">\n<p data-start=\"1366\" data-end=\"1427\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">(a,b)\u2208R(a, b) \\in R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0939\u0948, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">(b,a)\u2209R(b, a) \\notin R<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\"><span class=\"mord\">\u2208<\/span><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"llap\"><span class=\"inner\"><span class=\"mord\">\/<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<\/blockquote>\n<h4 data-start=\"1429\" data-end=\"1475\"><strong data-start=\"1434\" data-end=\"1473\">Example 1: &#8220;Less Than Relation (&lt;)&#8221;<\/strong><\/h4>\n<ul data-start=\"1476\" data-end=\"1614\">\n<li data-start=\"1476\" data-end=\"1528\">\u092f\u0926\u093f <strong data-start=\"1482\" data-end=\"1491\">a &lt; b<\/strong> \u0939\u0948, \u0924\u094b <strong data-start=\"1499\" data-end=\"1508\">b &lt; a<\/strong> \u0915\u092d\u0940 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e\u0964<\/li>\n<li data-start=\"1529\" data-end=\"1575\">\u0909\u0926\u093e\u0939\u0930\u0923: <span class=\"katex\"><span class=\"katex-mathml\">3&lt;73 &lt; 7<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><\/span><\/span><\/span>, \u0932\u0947\u0915\u093f\u0928 <span class=\"katex\"><span class=\"katex-mathml\">7&lt;37 &lt; 3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span> \u0917\u0932\u0924 \u0939\u0948\u0964<\/li>\n<li data-start=\"1576\" data-end=\"1614\">\u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0938\u0902\u092c\u0902\u0927 <strong data-start=\"1594\" data-end=\"1611\">Asymmetric \u0939\u0948<\/strong>\u0964<\/li>\n<\/ul>\n<h4 data-start=\"1616\" data-end=\"1673\"><strong data-start=\"1621\" data-end=\"1671\">Example 2: &#8220;Precedence Relation in Scheduling&#8221;<\/strong><\/h4>\n<ul data-start=\"1674\" data-end=\"1917\">\n<li data-start=\"1674\" data-end=\"1771\">\u092f\u0926\u093f <strong data-start=\"1680\" data-end=\"1723\">\u091f\u093e\u0938\u094d\u0915 A \u091f\u093e\u0938\u094d\u0915 B \u0938\u0947 \u092a\u0939\u0932\u0947 \u092a\u0942\u0930\u093e \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f<\/strong>, \u0924\u094b <strong data-start=\"1728\" data-end=\"1768\">\u091f\u093e\u0938\u094d\u0915 B \u091f\u093e\u0938\u094d\u0915 A \u0938\u0947 \u092a\u0939\u0932\u0947 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e<\/strong>\u0964<\/li>\n<li data-start=\"1772\" data-end=\"1884\">\u091c\u0948\u0938\u0947, \u0905\u0917\u0930 <strong data-start=\"1784\" data-end=\"1809\">Exam \u0938\u0947 \u092a\u0939\u0932\u0947 Revision<\/strong> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f, \u0924\u094b <strong data-start=\"1825\" data-end=\"1881\">Revision \u0915\u0947 \u092c\u093e\u0926 Exam \u0939\u0940 \u0939\u094b\u0917\u093e, Exam \u092a\u0939\u0932\u0947 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e<\/strong>\u0964<\/li>\n<li data-start=\"1885\" data-end=\"1917\">\u0907\u0938\u0932\u093f\u090f, \u092f\u0939 <strong data-start=\"1897\" data-end=\"1914\">Asymmetric \u0939\u0948<\/strong>\u0964<\/li>\n<\/ul>\n<h3 data-start=\"1924\" data-end=\"1969\"><strong data-start=\"1928\" data-end=\"1967\">\u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e (Comparison Table)<\/strong><\/h3>\n<div class=\"overflow-x-auto contain-inline-size\">\n<table data-start=\"1971\" data-end=\"2346\">\n<thead data-start=\"1971\" data-end=\"2023\">\n<tr data-start=\"1971\" data-end=\"2023\">\n<th data-start=\"1971\" data-end=\"1991\"><strong data-start=\"1973\" data-end=\"1990\">Relation Type<\/strong><\/th>\n<th data-start=\"1991\" data-end=\"2008\"><strong data-start=\"1993\" data-end=\"2007\">Definition<\/strong><\/th>\n<th data-start=\"2008\" data-end=\"2023\"><strong data-start=\"2010\" data-end=\"2021\">Example<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"2072\" data-end=\"2346\">\n<tr data-start=\"2072\" data-end=\"2164\">\n<td><strong data-start=\"2074\" data-end=\"2087\">Symmetric<\/strong><\/td>\n<td>\u092f\u0926\u093f (a, b) \u2208 R \u0924\u094b (b, a) \u092d\u0940 \u2208 R<\/td>\n<td>\u0926\u094b\u0938\u094d\u0924\u0940 (Friendship), \u0938\u092e\u093e\u0928\u0924\u093e (Equality)<\/td>\n<\/tr>\n<tr data-start=\"2165\" data-end=\"2255\">\n<td><strong data-start=\"2167\" data-end=\"2185\">Anti-Symmetric<\/strong><\/td>\n<td>\u092f\u0926\u093f (a, b) \u2208 R \u0914\u0930 (b, a) \u2208 R, \u0924\u094b a = b<\/td>\n<td>\u0938\u092c\u0938\u0947\u091f (\u2286), \u0935\u093f\u092d\u093e\u091c\u094d\u092f\u0924\u093e (<\/td>\n<\/tr>\n<tr data-start=\"2256\" data-end=\"2346\">\n<td><strong data-start=\"2258\" data-end=\"2272\">Asymmetric<\/strong><\/td>\n<td>\u092f\u0926\u093f (a, b) \u2208 R \u0924\u094b (b, a) \u2209 R<\/td>\n<td>\u091b\u094b\u091f\u093e-\u092c\u0921\u093c\u093e (&lt;), \u092a\u094d\u0930\u093e\u0925\u092e\u093f\u0915\u0924\u093e (Precedence)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3 data-start=\"2353\" data-end=\"2371\"><strong data-start=\"2357\" data-end=\"2369\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/strong><\/h3>\n<ul data-start=\"2372\" data-end=\"2610\">\n<li data-start=\"2372\" data-end=\"2453\"><strong data-start=\"2374\" data-end=\"2451\">Symmetric \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u092e\u0947\u0902 \u092f\u0926\u093f \u090f\u0915 \u091c\u094b\u0921\u093c\u0940 \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u0940 \u0909\u0932\u094d\u091f\u0940 \u091c\u094b\u0921\u093c\u0940 \u092d\u0940 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/strong><\/li>\n<li data-start=\"2454\" data-end=\"2535\"><strong data-start=\"2456\" data-end=\"2533\">Anti-Symmetric \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u092e\u0947\u0902 \u092f\u0926\u093f \u0926\u094b \u091c\u094b\u0921\u093c\u0940 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902, \u0924\u094b \u0935\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0928\u0947 \u091a\u093e\u0939\u093f\u090f\u0964<\/strong><\/li>\n<li data-start=\"2536\" data-end=\"2610\"><strong data-start=\"2538\" data-end=\"2608\">Asymmetric \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u092e\u0947\u0902 \u0915\u092d\u0940 \u092d\u0940 \u0926\u094b\u0928\u094b\u0902 \u0926\u093f\u0936\u093e\u0913\u0902 \u092e\u0947\u0902 \u0938\u0902\u092c\u0902\u0927 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e\u0964<\/strong><\/li>\n<\/ul>\n<p data-start=\"2617\" data-end=\"2689\" data-is-last-node=\"\" data-is-only-node=\"\"><strong data-start=\"2617\" data-end=\"2689\" data-is-last-node=\"\">GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u0932\u093f\u090f \u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0914\u0930 \u0905\u0927\u093f\u0915 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0914\u0930 \u0939\u0932 \u0915\u0940 \u091c\u0930\u0942\u0930\u0924 \u0939\u0948?<\/strong><\/p>\n<h3 data-start=\"2617\" data-end=\"2689\">Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry.<\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\">B.A.(Prog) Mathematics Discipline Specific Course (DSC-1)<\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/dpvipracollege.ac.in\/wp-content\/uploads\/2023\/01\/Discrete-Mathematical-Structures-2nd-Ed.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematical Structures<\/a><\/h3>\n<p data-start=\"0\" data-end=\"224\">Here is a clear and <strong data-start=\"20\" data-end=\"60\">easy-to-understand Hindi explanation<\/strong> of <strong data-start=\"64\" data-end=\"77\">Symmetric<\/strong>, <strong data-start=\"79\" data-end=\"97\">Anti-Symmetric<\/strong>, and <strong data-start=\"103\" data-end=\"127\">Asymmetric Relations<\/strong> with <strong data-start=\"133\" data-end=\"145\">examples<\/strong>, useful for <strong data-start=\"158\" data-end=\"166\">GATE<\/strong>, <strong data-start=\"168\" data-end=\"175\">BSc<\/strong>, <strong data-start=\"177\" data-end=\"187\">B.Tech<\/strong>, or any Discrete Mathematics course.<\/p>\n<hr data-start=\"226\" data-end=\"229\" \/>\n<h2 data-start=\"231\" data-end=\"282\">\ud83d\udcd8 <strong data-start=\"237\" data-end=\"280\">Part 07 \u2013 Discrete Mathematics for GATE<\/strong><\/h2>\n<h3 data-start=\"283\" data-end=\"370\">\ud83d\udd01 <strong data-start=\"290\" data-end=\"370\">Symmetric, Anti-Symmetric, and Asymmetric Relations with Examples (in Hindi)<\/strong><\/h3>\n<hr data-start=\"372\" data-end=\"375\" \/>\n<h2 data-start=\"377\" data-end=\"420\">1\ufe0f\u20e3 <strong data-start=\"384\" data-end=\"420\">Symmetric Relation (\u0938\u093e\u092e\u094d\u092f \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n<h3 data-start=\"422\" data-end=\"437\">\ud83d\udcd6 \u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/h3>\n<p data-start=\"438\" data-end=\"443\">\u092f\u0926\u093f<\/p>\n<blockquote data-start=\"444\" data-end=\"510\">\n<p data-start=\"446\" data-end=\"510\"><strong data-start=\"446\" data-end=\"473\">(a, b) \u2208 R \u21d2 (b, a) \u2208 R<\/strong><br data-start=\"473\" data-end=\"476\" \/>\u0924\u094b \u0930\u093f\u0932\u0947\u0936\u0928 <strong data-start=\"486\" data-end=\"499\">Symmetric<\/strong> \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/blockquote>\n<h3 data-start=\"512\" data-end=\"525\">\u2705 \u0909\u0926\u093e\u0939\u0930\u0923:<\/h3>\n<ul data-start=\"526\" data-end=\"650\">\n<li data-start=\"526\" data-end=\"591\">\n<p data-start=\"528\" data-end=\"591\">\u0926\u094b\u0938\u094d\u0924\u0940 \u0915\u093e \u0938\u0902\u092c\u0902\u0927:<br data-start=\"544\" data-end=\"547\" \/>\u092f\u0926\u093f A, B \u0915\u093e \u0926\u094b\u0938\u094d\u0924 \u0939\u0948 \u21d2 B \u092d\u0940 A \u0915\u093e \u0926\u094b\u0938\u094d\u0924 \u0939\u0948\u0964<\/p>\n<\/li>\n<li data-start=\"593\" data-end=\"650\">\n<p data-start=\"595\" data-end=\"650\">Relation R = { (1, 2), (2, 1), (3, 3) } \u2192 Symmetric \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"652\" data-end=\"655\" \/>\n<h2 data-start=\"657\" data-end=\"712\">2\ufe0f\u20e3 <strong data-start=\"664\" data-end=\"712\">Anti-Symmetric Relation (\u0935\u093f\u0930\u094b\u0927\u0940-\u0938\u093e\u092e\u094d\u092f \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n<h3 data-start=\"714\" data-end=\"729\">\ud83d\udcd6 \u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/h3>\n<p data-start=\"730\" data-end=\"735\">\u092f\u0926\u093f<\/p>\n<blockquote data-start=\"736\" data-end=\"814\">\n<p data-start=\"738\" data-end=\"814\"><strong data-start=\"738\" data-end=\"774\">(a, b) \u2208 R \u0914\u0930 (b, a) \u2208 R \u21d2 a = b<\/strong><br data-start=\"774\" data-end=\"777\" \/>\u0924\u094b \u0930\u093f\u0932\u0947\u0936\u0928 <strong data-start=\"787\" data-end=\"805\">Anti-Symmetric<\/strong> \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/blockquote>\n<h3 data-start=\"816\" data-end=\"829\">\u2705 \u0909\u0926\u093e\u0939\u0930\u0923:<\/h3>\n<ul data-start=\"830\" data-end=\"1011\">\n<li data-start=\"830\" data-end=\"913\">\n<p data-start=\"832\" data-end=\"913\">\u2264 (less than or equal to) \u0915\u093e \u0938\u0902\u092c\u0902\u0927:<br data-start=\"867\" data-end=\"870\" \/>\u0905\u0917\u0930 a \u2264 b \u0914\u0930 b \u2264 a \u21d2 \u0924\u094b a = b \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<\/li>\n<li data-start=\"915\" data-end=\"1011\">\n<p data-start=\"917\" data-end=\"1011\">Relation R = { (1, 1), (2, 2), (2, 3) } \u2192 Anti-Symmetric \u0939\u0948<br data-start=\"976\" data-end=\"979\" \/>(\u0915\u094d\u092f\u094b\u0902\u0915\u093f (3, 2) \u0907\u0938\u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u0948)<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1013\" data-end=\"1016\" \/>\n<h2 data-start=\"1018\" data-end=\"1063\">3\ufe0f\u20e3 <strong data-start=\"1025\" data-end=\"1063\">Asymmetric Relation (\u0905\u0938\u092e\u092e\u093f\u0924 \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n<h3 data-start=\"1065\" data-end=\"1080\">\ud83d\udcd6 \u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/h3>\n<p data-start=\"1081\" data-end=\"1086\">\u092f\u0926\u093f<\/p>\n<blockquote data-start=\"1087\" data-end=\"1152\">\n<p data-start=\"1089\" data-end=\"1152\"><strong data-start=\"1089\" data-end=\"1116\">(a, b) \u2208 R \u21d2 (b, a) \u2209 R<\/strong><br data-start=\"1116\" data-end=\"1119\" \/>\u0924\u094b \u0930\u093f\u0932\u0947\u0936\u0928 <strong data-start=\"1129\" data-end=\"1143\">Asymmetric<\/strong> \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/blockquote>\n<h3 data-start=\"1154\" data-end=\"1167\">\u2705 \u0909\u0926\u093e\u0939\u0930\u0923:<\/h3>\n<ul data-start=\"1168\" data-end=\"1321\">\n<li data-start=\"1168\" data-end=\"1237\">\n<p data-start=\"1170\" data-end=\"1237\">&#8220;is parent of&#8221;<br data-start=\"1184\" data-end=\"1187\" \/>\u0905\u0917\u0930 A, B \u0915\u093e \u092a\u093f\u0924\u093e \u0939\u0948 \u21d2 B, A \u0915\u093e \u092a\u093f\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e\u0964<\/p>\n<\/li>\n<li data-start=\"1239\" data-end=\"1321\">\n<p data-start=\"1241\" data-end=\"1321\">Relation R = { (1, 2), (2, 3) } \u2192 Asymmetric \u0939\u0948<br data-start=\"1288\" data-end=\"1291\" \/>(\u0915\u094b\u0908 \u092d\u0940 \u0909\u0932\u094d\u091f\u093e \u091c\u094b\u0921\u093c\u093e \u0928\u0939\u0940\u0902 \u0939\u0948)<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1323\" data-end=\"1326\" \/>\n<h2 data-start=\"1328\" data-end=\"1370\">\ud83d\udcca <strong data-start=\"1334\" data-end=\"1370\">Difference Chart (\u0924\u0941\u0932\u0928\u093e \u0924\u093e\u0932\u093f\u0915\u093e):<\/strong><\/h2>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"1372\" data-end=\"1688\">\n<thead data-start=\"1372\" data-end=\"1440\">\n<tr data-start=\"1372\" data-end=\"1440\">\n<th data-start=\"1372\" data-end=\"1390\" data-col-size=\"sm\">\u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u092a\u094d\u0930\u0915\u093e\u0930<\/th>\n<th data-start=\"1390\" data-end=\"1397\" data-col-size=\"sm\">\u0928\u093f\u092f\u092e<\/th>\n<th data-start=\"1397\" data-end=\"1406\" data-col-size=\"sm\">\u0909\u0926\u093e\u0939\u0930\u0923<\/th>\n<th data-start=\"1406\" data-end=\"1440\" data-col-size=\"sm\">\u0915\u094d\u092f\u093e (a = b) \u0936\u093e\u092e\u093f\u0932 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948?<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1508\" data-end=\"1688\">\n<tr data-start=\"1508\" data-end=\"1560\">\n<td data-start=\"1508\" data-end=\"1520\" data-col-size=\"sm\">Symmetric<\/td>\n<td data-col-size=\"sm\" data-start=\"1520\" data-end=\"1538\">(a, b) \u21d2 (b, a)<\/td>\n<td data-col-size=\"sm\" data-start=\"1538\" data-end=\"1553\">\u0926\u094b\u0938\u094d\u0924\u0940, \u0936\u093e\u0926\u0940<\/td>\n<td data-col-size=\"sm\" data-start=\"1553\" data-end=\"1560\">\u0939\u093e\u0901<\/td>\n<\/tr>\n<tr data-start=\"1561\" data-end=\"1619\">\n<td data-start=\"1561\" data-end=\"1578\" data-col-size=\"sm\">Anti-Symmetric<\/td>\n<td data-col-size=\"sm\" data-start=\"1578\" data-end=\"1605\">(a, b) \u0914\u0930 (b, a) \u21d2 a = b<\/td>\n<td data-col-size=\"sm\" data-start=\"1605\" data-end=\"1612\">\u2264, \u2286<\/td>\n<td data-col-size=\"sm\" data-start=\"1612\" data-end=\"1619\">\u0939\u093e\u0901<\/td>\n<\/tr>\n<tr data-start=\"1620\" data-end=\"1688\">\n<td data-start=\"1620\" data-end=\"1633\" data-col-size=\"sm\">Asymmetric<\/td>\n<td data-col-size=\"sm\" data-start=\"1633\" data-end=\"1656\">(a, b) \u21d2 (b, a) \u0928\u0939\u0940\u0902<\/td>\n<td data-col-size=\"sm\" data-start=\"1656\" data-end=\"1680\">\u092a\u093f\u0924\u093e-\u092a\u0941\u0924\u094d\u0930, \u092c\u0921\u093c\u093e-\u091b\u094b\u091f\u093e<\/td>\n<td data-col-size=\"sm\" data-start=\"1680\" data-end=\"1688\">\u0928\u0939\u0940\u0902<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<hr data-start=\"1690\" data-end=\"1693\" \/>\n<h2 data-start=\"1695\" data-end=\"1723\">\ud83d\udca1 <strong data-start=\"1701\" data-end=\"1723\">GATE \u0915\u0947 \u0932\u093f\u090f \u091f\u093f\u092a\u094d\u0938:<\/strong><\/h2>\n<ul data-start=\"1724\" data-end=\"1892\">\n<li data-start=\"1724\" data-end=\"1781\">\n<p data-start=\"1726\" data-end=\"1781\"><strong data-start=\"1726\" data-end=\"1739\">Symmetric<\/strong> \u092e\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u0926\u093f\u0936\u093e\u0913\u0902 \u092e\u0947\u0902 \u0930\u093f\u0932\u0947\u0936\u0928 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<\/li>\n<li data-start=\"1782\" data-end=\"1847\">\n<p data-start=\"1784\" data-end=\"1847\"><strong data-start=\"1784\" data-end=\"1802\">Anti-Symmetric<\/strong> \u092e\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u0924\u092d\u0940 \u091c\u092c a = b\u0964<\/p>\n<\/li>\n<li data-start=\"1848\" data-end=\"1892\">\n<p data-start=\"1850\" data-end=\"1892\"><strong data-start=\"1850\" data-end=\"1864\">Asymmetric<\/strong> \u092e\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u0915\u092d\u0940 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u0947\u0964<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1894\" data-end=\"1897\" \/>\n<p data-start=\"1899\" data-end=\"1962\">\u2705 <strong data-start=\"1901\" data-end=\"1941\">Practice Questions \u0915\u0947 \u0932\u093f\u090f \u0924\u0948\u092f\u093e\u0930 \u0939\u0942\u0901!<\/strong><br data-start=\"1941\" data-end=\"1944\" \/>\u091a\u093e\u0939\u0947\u0902 \u0924\u094b \u092e\u0948\u0902 \u0907\u0938\u0915\u093e:<\/p>\n<ul data-start=\"1963\" data-end=\"2065\">\n<li data-start=\"1963\" data-end=\"1993\">\n<p data-start=\"1965\" data-end=\"1993\"><strong data-start=\"1965\" data-end=\"1991\">Practice Worksheet PDF<\/strong><\/p>\n<\/li>\n<li data-start=\"1994\" data-end=\"2029\">\n<p data-start=\"1996\" data-end=\"2029\"><strong data-start=\"1996\" data-end=\"2027\">Short Video Script in Hindi<\/strong><\/p>\n<\/li>\n<li data-start=\"2030\" data-end=\"2065\">\n<p data-start=\"2032\" data-end=\"2065\"><strong data-start=\"2032\" data-end=\"2048\">MCQ for GATE<\/strong> \u092d\u0940 \u092c\u0928\u093e \u0938\u0915\u0924\u093e \u0939\u0942\u0901\u0964<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2067\" data-end=\"2088\" data-is-last-node=\"\" data-is-only-node=\"\">\u092c\u094b\u0932\u093f\u090f, \u0915\u0948\u0938\u0947 \u092e\u0926\u0926 \u0915\u0930\u0942\u0901?<\/p>\n<h3 data-start=\"2067\" data-end=\"2088\"><a href=\"https:\/\/web.stanford.edu\/class\/cs103x\/cs103x-notes.pdf\" target=\"_blank\" rel=\"noopener\">Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry.<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Part 07-Discrete Mathematics for gate- Example based on symmetry anti-symmetry and asymmetry. [fvplayer id=&#8221;246&#8243;] Part 07 &#8211; Discrete Mathematics for GATE: Examples on Symmetry, Anti-Symmetry, and Asymmetry 1. Symmetric Relation (\u0938\u092e\u092e\u093f\u0924 \u0938\u0902\u092c\u0902\u0927) \u092f\u0926\u093f (a,b)\u2208R(a, b) \\in R(a,b)\u2208R \u0939\u0948, \u0924\u094b (b,a)\u2208R(b, a) \\in R(b,a)\u2208R \u092d\u0940 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 Example 1: &#8220;Friendship Relation&#8221; \u0905\u0917\u0930 \u0930\u093e\u092e \u0914\u0930 \u0936\u094d\u092f\u093e\u092e \u0926\u094b\u0938\u094d\u0924 [&hellip;]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[76],"tags":[],"class_list":["post-3087","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3087","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3087"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3087\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3087"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3087"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3087"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}