{"id":3116,"date":"2025-06-05T10:50:14","date_gmt":"2025-06-05T10:50:14","guid":{"rendered":"https:\/\/diznr.com\/?p=3116"},"modified":"2025-06-05T10:50:14","modified_gmt":"2025-06-05T10:50:14","slug":"day-02-discrete-mathematics-for-gate-in-hindi-properties-of-relations-inverse-complement","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-02-discrete-mathematics-for-gate-in-hindi-properties-of-relations-inverse-complement\/","title":{"rendered":"Day 02 &#8211; Discrete mathematics for gate in Hindi &#8211; Properties of Relations ,Inverse Complement."},"content":{"rendered":"<p>Day 02 &#8211; Discrete mathematics for gate in Hindi &#8211; Properties of Relations ,Inverse Complement.<\/p>\n<p>[fvplayer id=&#8221;260&#8243;]<\/p>\n<p>\u092f\u0939\u093e\u0901 <strong>GATE \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0938\u093e\u0907\u0902\u0938<\/strong> \u0915\u0947 \u0932\u093f\u090f <strong>Discrete Mathematics<\/strong> \u0915\u0947 \u091f\u0949\u092a\u093f\u0915 <strong>&#8220;Relations&#8221;<\/strong> \u0915\u0947 \u0905\u0902\u0924\u0930\u094d\u0917\u0924 <strong>Properties<\/strong>, <strong>Inverse Relation<\/strong>, \u0914\u0930 <strong>Complement of Relation<\/strong> \u0915\u093e \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0914\u0930 \u0938\u0930\u0932 \u0935\u093f\u0935\u0930\u0923 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udcd8 <strong>Relations \u0915\u0940 Properties (\u0917\u0941\u0923)<\/strong><\/h2>\n<p>\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0938\u0947\u091f <span class=\"katex\">AA<\/span> \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u090f\u0915 \u0938\u0902\u092c\u0902\u0927 <span class=\"katex\">RR<\/span> \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0941\u0923 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ol>\n<li><strong>Reflexive (\u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0928\u0940\u092f):<\/strong> \u0939\u0930 \u0924\u0924\u094d\u0935 <span class=\"katex\">a\u2208Aa \\in A<\/span> \u0915\u0947 \u0932\u093f\u090f <span class=\"katex\">(a,a)\u2208R(a, a) \\in R<\/span> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/li>\n<li><strong>Symmetric (\u0938\u092e\u092e\u093f\u0924):<\/strong> \u092f\u0926\u093f <span class=\"katex\">(a,b)\u2208R(a, b) \\in R<\/span>, \u0924\u094b <span class=\"katex\">(b,a)\u2208R(b, a) \\in R<\/span> \u092d\u0940 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/li>\n<li><strong>Transitive (\u0938\u093e\u0902\u0915\u094d\u0930\u093e\u092e\u0915):<\/strong> \u092f\u0926\u093f <span class=\"katex\">(a,b)\u2208R(a, b) \\in R<\/span> \u0914\u0930 <span class=\"katex\">(b,c)\u2208R(b, c) \\in R<\/span>, \u0924\u094b <span class=\"katex\">(a,c)\u2208R(a, c) \\in R<\/span> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/li>\n<li><strong>Antisymmetric (\u092a\u094d\u0930\u0924\u093f\u0938\u092e\u092e\u093f\u0924):<\/strong> \u092f\u0926\u093f <span class=\"katex\">(a,b)\u2208R(a, b) \\in R<\/span> \u0914\u0930 <span class=\"katex\">(b,a)\u2208R(b, a) \\in R<\/span>, \u0924\u094b <span class=\"katex\">a=ba = b<\/span> \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/li>\n<\/ol>\n<hr \/>\n<h2>\ud83d\udd01 <strong>Inverse Relation (\u0909\u0932\u094d\u091f\u093e \u0938\u0902\u092c\u0902\u0927)<\/strong><\/h2>\n<p>\u092f\u0926\u093f <span class=\"katex\">RR<\/span> \u090f\u0915 \u0938\u0902\u092c\u0902\u0927 \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u093e \u0909\u0932\u094d\u091f\u093e \u0938\u0902\u092c\u0902\u0927 <span class=\"katex\">R\u22121R^{-1}<\/span> \u0909\u0928 \u0938\u092d\u0940 \u092f\u0941\u0917\u094d\u092e\u094b\u0902 \u0915\u093e \u0938\u0947\u091f \u0939\u0948 \u091c\u0939\u093e\u0901 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span class=\"katex\">(a,b)\u2208R(a, b) \\in R<\/span> \u0915\u0947 \u0932\u093f\u090f <span class=\"katex\">(b,a)\u2208R\u22121(b, a) \\in R^{-1}<\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/p>\n<p>\u092f\u0926\u093f <span class=\"katex\">R={(1,2),(3,4)}R = \\{(1, 2), (3, 4)\\}<\/span>, \u0924\u094b <span class=\"katex\">R\u22121={(2,1),(4,3)}R^{-1} = \\{(2, 1), (4, 3)\\}<\/span> \u0939\u094b\u0917\u093e\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udd04 <strong>Complement of a Relation (\u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u092a\u0942\u0930\u0915)<\/strong><\/h2>\n<p>\u092f\u0926\u093f <span class=\"katex\">AA<\/span> \u090f\u0915 \u0938\u0947\u091f \u0939\u0948 \u0914\u0930 <span class=\"katex\">RR<\/span> \u0909\u0938 \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u090f\u0915 \u0938\u0902\u092c\u0902\u0927 \u0939\u0948, \u0924\u094b <span class=\"katex\">RR<\/span> \u0915\u093e \u092a\u0942\u0930\u0915 <span class=\"katex\">R\u203e\\overline{R}<\/span> \u0909\u0928 \u0938\u092d\u0940 \u092f\u0941\u0917\u094d\u092e\u094b\u0902 \u0915\u093e \u0938\u0947\u091f \u0939\u0948 \u091c\u094b <span class=\"katex\">A\u00d7AA \\times A<\/span> \u092e\u0947\u0902 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 <span class=\"katex\">RR<\/span> \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964<\/p>\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/p>\n<p>\u092f\u0926\u093f <span class=\"katex\">A={1,2}A = \\{1, 2\\}<\/span> \u0914\u0930 <span class=\"katex\">R={(1,1)}R = \\{(1, 1)\\}<\/span>, \u0924\u094b <span class=\"katex\">A\u00d7A={(1,1),(1,2),(2,1),(2,2)}A \\times A = \\{(1, 1), (1, 2), (2, 1), (2, 2)\\}<\/span> \u0914\u0930 <span class=\"katex\">R\u203e={(1,2),(2,1),(2,2)}\\overline{R} = \\{(1, 2), (2, 1), (2, 2)\\}<\/span> \u0939\u094b\u0917\u093e\u0964<\/p>\n<hr \/>\n<h2>\ud83c\udfa5 <strong>\u0935\u0940\u0921\u093f\u092f\u094b \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932\u094d\u0938 (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902)<\/strong><\/h2>\n<p>\u0907\u0928 \u0935\u093f\u0937\u092f\u094b\u0902 \u0915\u094b \u0914\u0930 \u092c\u0947\u0939\u0924\u0930 \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0935\u0940\u0921\u093f\u092f\u094b \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932\u094d\u0938 \u0926\u0947\u0916\u0947\u0902:<\/p>\n<ol>\n<li>Complement and Inverse Of A Relation In Discrete Mathematics In Hindi<\/li>\n<li>Operations on Relations (Union, Intersection, Complement, Inverse) &#8211; Discrete Mathematics in Hindi<\/li>\n<li>Complement and Converse Relations &#8211; Discrete Mathematics in Hindi<\/li>\n<\/ol>\n<hr \/>\n<p>\u092f\u0926\u093f \u0906\u092a \u0907\u0928 \u0935\u093f\u0937\u092f\u094b\u0902 \u092a\u0930 \u092a\u0940\u0921\u0940\u090f\u092b \u0928\u094b\u091f\u094d\u0938, \u0905\u092d\u094d\u092f\u093e\u0938 \u092a\u094d\u0930\u0936\u094d\u0928 \u092f\u093e \u0905\u0928\u094d\u092f \u0938\u0939\u093e\u092f\u0924\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0943\u092a\u092f\u093e \u092c\u0924\u093e\u090f\u0902\u0964 \u092e\u0948\u0902 \u0906\u092a\u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0915\u0947 \u0932\u093f\u090f \u0924\u0948\u092f\u093e\u0930 \u0939\u0942\u0901\u0964<\/p>\n<h3><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Day 02 &#8211; Discrete mathematics for gate in Hindi &#8211; Properties of Relations ,Inverse Complement.<\/a><\/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<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/niamt.ac.in\/WriteReadData\/Mathematics%20(Discrete%20Structure).pdf\" target=\"_blank\" rel=\"noopener\">Mathematics (Discrete Structure).pdf<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/uou.ac.in\/sites\/default\/files\/slm\/MCS-501.pdf\" target=\"_blank\" rel=\"noopener\">Title Discrete Mathematics Author Prof. Abhay Saxena &#8230;<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/mdu.ac.in\/UpFiles\/UpPdfFiles\/2020\/Jan\/Advance_Discrete_MAths_com.pdf\" target=\"_blank\" rel=\"noopener\">ADVANCED DISCRETE MATHEMATICS MM-504 &amp; 505 ( &#8230;<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/faculty.ksu.edu.sa\/sites\/default\/files\/rosen_discrete_mathematics_and_its_applications_7th_edition.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics and Its Applications, Seventh Edition<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Day 02 &#8211; Discrete mathematics for gate in Hindi &#8211; Properties of Relations ,Inverse Complement. [fvplayer id=&#8221;260&#8243;] \u092f\u0939\u093e\u0901 GATE \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0938\u093e\u0907\u0902\u0938 \u0915\u0947 \u0932\u093f\u090f Discrete Mathematics \u0915\u0947 \u091f\u0949\u092a\u093f\u0915 &#8220;Relations&#8221; \u0915\u0947 \u0905\u0902\u0924\u0930\u094d\u0917\u0924 Properties, Inverse Relation, \u0914\u0930 Complement of Relation \u0915\u093e \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0914\u0930 \u0938\u0930\u0932 \u0935\u093f\u0935\u0930\u0923 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0939\u0948\u0964 \ud83d\udcd8 Relations \u0915\u0940 Properties (\u0917\u0941\u0923) \u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0938\u0947\u091f AA [&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-3116","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3116","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=3116"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3116\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}