Discrete Mathematics questions – GATE 2015 Let R be the relation on the set of positive integer.<\/p>\n
[fvplayer id=”244″]<\/p>\n
Great! You’re referring to a Discrete Mathematics<\/strong> question likely from the GATE 2025<\/strong> syllabus. You mentioned:<\/p>\n “Let RR<\/span>R<\/span><\/span><\/span><\/span> be the relation on the set of positive integers…”<\/p>\n<\/blockquote>\n Please provide the full question<\/strong>, including the definition of the relation RR<\/span>R<\/span><\/span><\/span><\/span>, and what the question is asking (e.g., Is RR<\/span>R<\/span><\/span><\/span><\/span> reflexive, symmetric, transitive? Find the number of equivalence classes? etc.)<\/p>\n Let RR<\/span>R<\/span><\/span><\/span><\/span> be a relation on the set of positive integers Z+\\mathbb{Z}^+<\/span>Z<\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, defined by:<\/p>\n (a,b)\u2208R\u2005\u200a\u27fa\u2005\u200aamod\u2009\u2009n=bmod\u2009\u2009n(a, b) \\in R \\iff a \\mod n = b \\mod n<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span>\u2208<\/span><\/span>R<\/span>\u27fa<\/span><\/span>a<\/span><\/span>mod<\/span><\/span>n<\/span>=<\/span><\/span>b<\/span><\/span>mod<\/span><\/span>n<\/span><\/span><\/span><\/span><\/p>\n Then RR<\/span>R<\/span><\/span><\/span><\/span> is:<\/p>\n<\/blockquote>\n Solution:<\/strong> Reflexive: Yes, because amod\u2009\u2009n=amod\u2009\u2009na \\mod n = a \\mod n<\/span>a<\/span><\/span>mod<\/span><\/span>n<\/span>=<\/span><\/span>a<\/span><\/span>mod<\/span><\/span>n<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n Symmetric: Yes, if a\u2261b(modn)a \\equiv b \\pmod{n}<\/span>a<\/span>\u2261<\/span><\/span>b<\/span><\/span>(<\/span>mod<\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span>, then b\u2261a(modn)b \\equiv a \\pmod{n}<\/span>b<\/span>\u2261<\/span><\/span>a<\/span><\/span>(<\/span>mod<\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n Transitive: Yes, if a\u2261b(modn)a \\equiv b \\pmod{n}<\/span>a<\/span>\u2261<\/span><\/span>b<\/span><\/span>(<\/span>mod<\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span> and b\u2261c(modn)b \\equiv c \\pmod{n}<\/span>b<\/span>\u2261<\/span><\/span>c<\/span><\/span>(<\/span>mod<\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span>, then a\u2261c(modn)a \\equiv c \\pmod{n}<\/span>a<\/span>\u2261<\/span><\/span>c<\/span><\/span>(<\/span>mod<\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n \u2705 Hence, it is an equivalence relation<\/strong><\/p>\n Please share the full question so I can give you a specific solution!<\/p>\n Discrete Mathematics questions – GATE 2015 Let R be the relation on the set of positive integer. [fvplayer id=”244″] Great! You’re referring to a Discrete Mathematics question likely from the GATE 2025 syllabus. You mentioned: “Let RRR be the relation on the set of positive integers…” Please provide the full question, including the definition of […]<\/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-3083","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3083","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=3083"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3083\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3083"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3083"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3083"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
In the meantime, here’s a general template for such problems:<\/h3>\n
Example Problem Format<\/strong><\/h4>\n
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This is the standard congruence modulo n<\/em> relation.<\/p>\n\n
\nDiscrete Mathematics questions – GATE 2025 Let R be the relation on the set of positive integer.<\/a><\/h3>\n
Problems on Discrete Mathematics1 (Part I)<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"