{"id":3111,"date":"2025-06-07T10:17:03","date_gmt":"2025-06-07T10:17:03","guid":{"rendered":"https:\/\/diznr.com\/?p=3111"},"modified":"2025-06-07T10:17:03","modified_gmt":"2025-06-07T10:17:03","slug":"day-02-discrete-mathematics-for-computer-science-in-hindi-type-of-relation-with-concept-basic","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-02-discrete-mathematics-for-computer-science-in-hindi-type-of-relation-with-concept-basic\/","title":{"rendered":"Day 02-Discrete mathematics for computer science in Hindi – Type of Relation with basic concept"},"content":{"rendered":"

Day 02-Discrete mathematics for computer science in Hindi – Type of Relation with basic concept<\/p>\n

[fvplayer id=”258″]<\/p>\n

\u092c\u093f\u0932\u0915\u0941\u0932! \u092f\u0939 \u0939\u0948 Day 02<\/strong> \u0915\u093e \u092a\u0942\u0930\u093e \u0928\u094b\u091f\u094d\u0938 \u0914\u0930 \u0938\u092e\u091d\u093e\u092f\u093e \u0939\u0941\u0906 \u092d\u093e\u0917 \u2014
Discrete Mathematics for Computer Science (CSE\/IT) in Hindi<\/strong><\/p>\n

\ud83d\udd39 \u091f\u0949\u092a\u093f\u0915: Types of Relations (\u0938\u0902\u092c\u0902\u0927 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930) \u0914\u0930 \u0909\u0938\u0915\u093e \u092c\u0947\u0938\u093f\u0915 \u0915\u0949\u0928\u094d\u0938\u0947\u092a\u094d\u091f<\/strong><\/h3>\n
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\ud83d\udcd8 \u0930\u093f\u0932\u0947\u0936\u0928 (Relation) \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/strong><\/h2>\n

\u0905\u0917\u0930 \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0926\u094b sets \u0939\u094b\u0902, A \u0914\u0930 B, \u0924\u094b \u0909\u0928\u0915\u093e Cartesian Product:<\/p>\n

A\u00d7B={(a,b)\u00a0\u2223\u00a0a\u2208A,b\u2208B}A \\times B = \\{ (a, b) \\ | \\ a \\in A, b \\in B \\}<\/span>A<\/span>\u00d7<\/span><\/span>B<\/span>=<\/span><\/span>{(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>\u00a0<\/span>\u2223<\/span>\u00a0<\/span>a<\/span>\u2208<\/span><\/span>A<\/span>,<\/span>b<\/span>\u2208<\/span><\/span>B<\/span>}<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u0905\u092c, \u0907\u0938 Cartesian Product \u0915\u093e \u0915\u094b\u0908 subset \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948 \u090f\u0915 Relation (R)<\/strong><\/p>\n

\ud83d\udc49 Relation: A \u0938\u0947 B \u0924\u0915 \u0915\u093f\u0938\u0940 \u0928\u093f\u092f\u092e \u092f\u093e \u0915\u0902\u0921\u0940\u0936\u0928 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 ordered pairs \u0915\u093e collection<\/p>\n

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\ud83d\udd22 Types of Relations (\u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930)<\/strong><\/h2>\n
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\n\n\n\n\n\n\n\n\n\n\n
\u0915\u094d\u0930.\u0938\u0902.<\/th>\n\u092a\u094d\u0930\u0915\u093e\u0930 (Type)<\/th>\n\u092a\u0930\u093f\u092d\u093e\u0937\u093e (Definition in Hindi)<\/th>\n<\/tr>\n<\/thead>\n
1\ufe0f\u20e3<\/td>\nReflexive Relation<\/td>\n\u0939\u0930 element \u0916\u0941\u0926 \u0938\u0947 related \u0939\u094b: (a,a)\u2208R(a, a) \\in R<\/span>(<\/span>a<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
2\ufe0f\u20e3<\/td>\nSymmetric Relation<\/td>\n\u0905\u0917\u0930 (a,b)\u2208R(a, b) \\in R<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span> \u0939\u0948 \u0924\u094b (b,a)\u2208R(b, a) \\in R<\/span>(<\/span>b<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span> \u092d\u0940 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f<\/td>\n<\/tr>\n
3\ufe0f\u20e3<\/td>\nAnti-Symmetric Relation<\/td>\n\u0905\u0917\u0930 (a,b)\u2208R(a, b) \\in R<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span> \u0914\u0930 (b,a)\u2208R(b, a) \\in R<\/span>(<\/span>b<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span>, \u0924\u094b a=ba = b<\/span>a<\/span>=<\/span><\/span>b<\/span><\/span><\/span><\/span> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f<\/td>\n<\/tr>\n
4\ufe0f\u20e3<\/td>\nTransitive Relation<\/td>\n\u0905\u0917\u0930 (a,b)\u2208R(a, b) \\in R<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span> \u0914\u0930 (b,c)\u2208R(b, c) \\in R<\/span>(<\/span>b<\/span>,<\/span>c<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span>, \u0924\u094b (a,c)\u2208R(a, c) \\in R<\/span>(<\/span>a<\/span>,<\/span>c<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span> \u092d\u0940 \u0939\u094b<\/td>\n<\/tr>\n
5\ufe0f\u20e3<\/td>\nEquivalence Relation<\/td>\n\u091c\u094b Reflexive + Symmetric + Transitive \u0939\u094b<\/td>\n<\/tr>\n
6\ufe0f\u20e3<\/td>\nIrreflexive Relation<\/td>\n\u0915\u094b\u0908 \u092d\u0940 element \u0916\u0941\u0926 \u0938\u0947 related \u0928 \u0939\u094b: (a,a)\u2209R(a, a) \\notin R<\/span>(<\/span>a<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span>\/<\/span><\/span><\/span><\/span><\/span><\/span><\/span>R<\/span><\/span><\/span><\/span><\/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\udd0d 1. Reflexive Relation (\u092a\u094d\u0930\u0924\u094d\u092f\u093e\u0935\u0930\u094d\u0924\u0940 \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n

\ud83d\udfe2 Definition: (a,a)\u2208R(a, a) \\in R<\/span>(<\/span>a<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span> \u2200 a \u2208 A
\u2705 Example: A = {1,2}, R = {(1,1), (2,2)} \u2014 Reflexive<\/p>\n

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\ud83d\udd0d 2. Symmetric Relation (\u0938\u093e\u092e\u094d\u092f \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n

\ud83d\udfe2 Definition: (a,b)\u2208R\u21d2(b,a)\u2208R(a, b) \\in R \\Rightarrow (b, a) \\in R<\/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><\/span><\/span><\/span>
\u2705 Example: {(1,2), (2,1)}
\u274c Not symmetric: {(1,2)} only<\/p>\n

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\ud83d\udd0d 3. Anti-Symmetric Relation (\u092a\u094d\u0930\u0924\u093f-\u0938\u093e\u092e\u094d\u092f \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n

\ud83d\udfe2 Definition: (a,b),(b,a)\u2208R\u21d2a=b(a,b), (b,a) \\in R \\Rightarrow a = b<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>,<\/span>(<\/span>b<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span><\/span>R<\/span>\u21d2<\/span><\/span>a<\/span>=<\/span><\/span>b<\/span><\/span><\/span><\/span>
\u2705 Example: {(1,1), (2,2), (1,2)}
\u274c {(1,2), (2,1)} \u2192 Not anti-symmetric<\/p>\n

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\ud83d\udd0d 4. Transitive Relation (\u0938\u093e\u0902\u0915\u094d\u0930\u093e\u092e\u0915 \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n

\ud83d\udfe2 Definition: (a,b),(b,c)\u2208R\u21d2(a,c)\u2208R(a,b), (b,c) \\in R \\Rightarrow (a,c) \\in R<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>,<\/span>(<\/span>b<\/span>,<\/span>c<\/span>)<\/span>\u2208<\/span><\/span>R<\/span>\u21d2<\/span><\/span>(<\/span>a<\/span>,<\/span>c<\/span>)<\/span>\u2208<\/span><\/span>R<\/span><\/span><\/span><\/span>
\u2705 Example: {(1,2), (2,3), (1,3)}<\/p>\n

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\ud83d\udd0d 5. Equivalence Relation (\u0938\u092e\u093e\u0928\u0924\u093e \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n

\ud83d\udc49 \u0935\u0939 relation \u091c\u094b \u0924\u0940\u0928\u094b\u0902 properties satisfy \u0915\u0930\u0924\u093e \u0939\u0948:<\/p>\n

\u2705 Reflexive
\u2705 Symmetric
\u2705 Transitive<\/p>\n

\u27a1\ufe0f Example: \u201cis equal to\u201d (=) relation<\/p>\n

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\ud83d\udd0d 6. Irreflexive Relation (\u0905\u092a\u094d\u0930\u0924\u094d\u092f\u093e\u0935\u0930\u094d\u0924\u0940 \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n

\ud83d\uded1 (a,a)\u2209R(a,a) \\notin R<\/span>(<\/span>a<\/span>,<\/span>a<\/span>)<\/span>\u2208<\/span>\/<\/span><\/span><\/span><\/span><\/span><\/span><\/span>R<\/span><\/span><\/span><\/span> \u2200 a \u2208 A
\u27a1\ufe0f Example: A = {1,2}, R = {(1,2), (2,1)} \u2014 Irreflexive<\/p>\n

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\ud83e\udde0 Visualization (Venn Diagram Style Explanation)<\/strong><\/h2>\n

You can visualize relation as arrows from elements to elements<\/strong>.
Symmetric \u2192 double-sided arrow
Transitive \u2192 chains
Reflexive \u2192 self-loops<\/p>\n

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\ud83e\uddea GATE \u0914\u0930 CS \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917:<\/strong><\/h2>\n
\n
\n\n\n\n\n\n\n\n\n\n
Concept<\/th>\nUse Area<\/th>\n<\/tr>\n<\/thead>\n
Reflexive<\/td>\nSet Theory, Database Relations<\/td>\n<\/tr>\n
Symmetric<\/td>\nUndirected Graphs<\/td>\n<\/tr>\n
Transitive<\/td>\nReachability in Graphs<\/td>\n<\/tr>\n
Anti-Symmetric<\/td>\nPartial Order Relations<\/td>\n<\/tr>\n
Equivalence<\/td>\nClassification, State Machines<\/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\udcdd Practice Example:<\/strong><\/h2>\n

Let A = {1, 2, 3}<\/p>\n

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

Q: \u092f\u0939 relation \u0915\u094c\u0928-\u0915\u094c\u0928 \u0938\u0940 property satisfy \u0915\u0930\u0924\u093e \u0939\u0948?<\/h3>\n

\ud83d\udd0e Reflexive? \u2705
\ud83d\udd0e Symmetric? \u2705
\ud83d\udd0e Transitive? \u274c
\ud83d\udc49 So, Not an Equivalence Relation<\/strong><\/p>\n

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\ud83d\udcda Extra Tip:<\/h2>\n

Equivalence Relation \u0938\u0947 \u092c\u0928\u0924\u093e \u0939\u0948:<\/p>\n

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Partition of Set<\/strong> \u2014 i.e., it divides the set into disjoint equivalence classes.<\/p>\n<\/blockquote>\n

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\ud83d\udce6 Conclusion:<\/h2>\n
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\n\n\n\n\n\n\n\n\n\n
Relation Type<\/th>\nSymbolic Rule<\/th>\n<\/tr>\n<\/thead>\n
Reflexive<\/td>\n(a,a) \u2208 R<\/td>\n<\/tr>\n
Symmetric<\/td>\n(a,b) \u2208 R \u21d2 (b,a) \u2208 R<\/td>\n<\/tr>\n
Anti-Symmetric<\/td>\n(a,b) \u2208 R \u2227 (b,a) \u2208 R \u21d2 a = b<\/td>\n<\/tr>\n
Transitive<\/td>\n(a,b), (b,c) \u2208 R \u21d2 (a,c) \u2208 R<\/td>\n<\/tr>\n
Equivalence<\/td>\nReflexive + Symmetric + Transitive<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u0915\u094d\u092f\u093e \u0906\u092a \u0907\u0938 \u091f\u0949\u092a\u093f\u0915 \u092a\u0930 PDF notes<\/strong>, video lecture (Hindi)<\/strong>, \u092f\u093e MCQ practice sheet<\/strong> \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902?<\/p>\n

Day 02-Discrete mathematics for computer science in Hindi – Type of Relation with basic concept<\/a><\/h3>\n

Mathematics for Computer Science – courses – MIT<\/a><\/h3>\n

ADVANCED DISCRETE MATHEMATICS MM-504 & 505 ( …<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Day 02-Discrete mathematics for computer science in Hindi – Type of Relation with basic concept [fvplayer id=”258″] \u092c\u093f\u0932\u0915\u0941\u0932! \u092f\u0939 \u0939\u0948 Day 02 \u0915\u093e \u092a\u0942\u0930\u093e \u0928\u094b\u091f\u094d\u0938 \u0914\u0930 \u0938\u092e\u091d\u093e\u092f\u093e \u0939\u0941\u0906 \u092d\u093e\u0917 \u2014Discrete Mathematics for Computer Science (CSE\/IT) in Hindi \ud83d\udd39 \u091f\u0949\u092a\u093f\u0915: Types of Relations (\u0938\u0902\u092c\u0902\u0927 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930) \u0914\u0930 \u0909\u0938\u0915\u093e \u092c\u0947\u0938\u093f\u0915 \u0915\u0949\u0928\u094d\u0938\u0947\u092a\u094d\u091f \ud83d\udcd8 \u0930\u093f\u0932\u0947\u0936\u0928 (Relation) \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? […]<\/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-3111","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3111","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=3111"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3111\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3111"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3111"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}