{"id":3107,"date":"2025-06-07T10:14:04","date_gmt":"2025-06-07T10:14:04","guid":{"rendered":"https:\/\/diznr.com\/?p=3107"},"modified":"2025-06-07T10:14:04","modified_gmt":"2025-06-07T10:14:04","slug":"day-02-discrete-mathematics-for-gate-in-hindi-symmeteric-relation-and-application-its","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-02-discrete-mathematics-for-gate-in-hindi-symmeteric-relation-and-application-its\/","title":{"rendered":"Day 02 – Discrete mathematics for gate in Hindi – Symmeteric Relation and it’s application."},"content":{"rendered":"

Day 02 – Discrete mathematics for gate in Hindi – Symmeteric Relation and it’s application.<\/p>\n

[fvplayer id=”256″]<\/p>\n

Here’s a detailed explanation of Symmetric Relation<\/strong> and its application, tailored for Day 02 of Discrete Mathematics for GATE (CSE\/IT)<\/strong>, explained in Hindi-English (Hinglish)<\/strong> for better understanding.<\/p>\n

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\ud83d\udcd8 Day 02 \u2013 Discrete Mathematics for GATE<\/h2>\n

\ud83d\udd39 Topic: Symmetric Relation (\u0938\u093e\u092e\u094d\u092f \u0938\u0902\u092c\u0902\u0927)<\/h3>\n
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\ud83d\udd0d 1. Symmetric Relation \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/strong><\/h2>\n

\ud83d\udd38 Definition (\u092a\u0930\u093f\u092d\u093e\u0937\u093e):<\/strong><\/h3>\n

\u090f\u0915 relation R<\/strong> \u0915\u094b Symmetric<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0905\u0917\u0930<\/strong>:<\/p>\n

For\u00a0all\u00a0a,b\u2208A,\u00a0\u0905\u0917\u0930\u00a0(a,b)\u2208R\u21d2(b,a)\u2208R\u00a0\u092d\u0940\u00a0\u0939\u094b\\text{For all } a, b \\in A, \\text{ \u0905\u0917\u0930 } (a, b) \\in R \\Rightarrow (b, a) \\in R \\text{ \u092d\u0940 \u0939\u094b}<\/span>For\u00a0all\u00a0<\/span><\/span>a<\/span>,<\/span>b<\/span>\u2208<\/span><\/span>A<\/span>,<\/span>\u00a0<\/span>\u0905\u0917\u0930<\/span>\u00a0<\/span><\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>\u2208<\/span><\/span>R<\/span>\u21d2<\/span><\/span>(<\/span>b<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span><\/span>R<\/span>\u00a0<\/span>\u092d\u0940<\/span>\u00a0<\/span>\u0939\u094b<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u092e\u0924\u0932\u092c: \u0905\u0917\u0930 A \u0928\u0947 B \u0915\u094b \u092a\u094d\u092f\u093e\u0930 \u0915\u093f\u092f\u093e, \u0924\u094b B \u0928\u0947 \u092d\u0940 A \u0915\u094b \u092a\u094d\u092f\u093e\u0930 \u0915\u093f\u092f\u093e \u2014 \u092f\u0947 \u090f\u0915 symmetric relation \u0939\u0948 \ud83d\ude0a<\/p>\n

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\ud83c\udfaf 2. \u0906\u0938\u093e\u0928 \u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/h2>\n

\u2714\ufe0f Example 1:<\/h3>\n

Let A = {1, 2, 3}<\/strong>
Let R = {(1, 1), (2, 2), (1, 2), (2, 1)}<\/strong><\/p>\n

\u2705 \u092f\u0939\u093e\u0901 (1, 2) \u0939\u0948 \u0924\u094b (2, 1) \u092d\u0940 \u0939\u0948 \u21d2 Symmetric Relation<\/strong><\/p>\n

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\u274c Example 2:<\/h3>\n

R = {(1, 2), (2, 3)}<\/p>\n

\u092f\u0939\u093e\u0901 (2, 1) \u0914\u0930 (3, 2) missing \u0939\u0948\u0902 \u21d2 Not symmetric<\/strong><\/p>\n

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\ud83e\udde0 3. Daily Life Example of Symmetric Relation:<\/strong><\/h2>\n
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\n\n\n\n\n\n\n\n
Relation<\/th>\nSymmetric?<\/th>\nWhy?<\/th>\n<\/tr>\n<\/thead>\n
“is sibling of” (\u092d\u093e\u0908\/\u092c\u0939\u0928 \u0939\u0948)<\/td>\n\u2705 Yes<\/td>\nA \u092d\u093e\u0908 \u0939\u0948 B \u0915\u093e, \u0924\u094b B \u092d\u0940 A \u0915\u093e \u092d\u093e\u0908<\/td>\n<\/tr>\n
“is father of” (\u092a\u093f\u0924\u093e \u0939\u0948)<\/td>\n\u274c No<\/td>\nA \u092a\u093f\u0924\u093e \u0939\u0948 B \u0915\u093e, B A \u0915\u093e \u0928\u0939\u0940\u0902<\/td>\n<\/tr>\n
“has same birthday as”<\/td>\n\u2705 Yes<\/td>\nA \u0915\u093e birthday B \u0915\u0947 \u091c\u0948\u0938\u093e \u0939\u0948 \u21d2 B \u0915\u093e \u092d\u0940 A \u091c\u0948\u0938\u093e<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\ud83d\udcd8 4. Representation (Matrix form \u092e\u0947\u0902):<\/strong><\/h2>\n

Let R be a relation on set A = {1, 2}<\/p>\n

If:<\/p>\n

R={(1,2),(2,1)}R = \\{(1, 2), (2, 1)\\}<\/span>R<\/span>=<\/span><\/span>{(<\/span>1<\/span>,<\/span>2<\/span>)<\/span>,<\/span>(<\/span>2<\/span>,<\/span>1<\/span>)}<\/span><\/span><\/span><\/span><\/span><\/p>\n

Then matrix form:<\/p>\n

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\n\n\n\n\n\n\n
<\/th>\n1<\/th>\n2<\/th>\n<\/tr>\n<\/thead>\n
1<\/td>\n0<\/td>\n1<\/td>\n<\/tr>\n
2<\/td>\n1<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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<\/div>\n<\/div>\n<\/div>\n<\/div>\n

\ud83d\udd04 Matrix is symmetric along diagonal<\/strong> \u21d2 R is symmetric<\/p>\n

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\ud83d\udd27 5. GATE \u092e\u0947\u0902 Use \u0914\u0930 Application:<\/strong><\/h2>\n