{"id":3060,"date":"2025-06-05T09:12:52","date_gmt":"2025-06-05T09:12:52","guid":{"rendered":"https:\/\/diznr.com\/?p=3060"},"modified":"2025-06-05T09:12:52","modified_gmt":"2025-06-05T09:12:52","slug":"discrete-mathematics-previous-year-gate-2021-equivalence-relation-let-r-and-s-be-any-two-2-equivalence","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/discrete-mathematics-previous-year-gate-2021-equivalence-relation-let-r-and-s-be-any-two-2-equivalence\/","title":{"rendered":"Discrete Mathematics previous year-GATE 2025 Equivalence relation Let R and S be any two equivalence."},"content":{"rendered":"

Discrete Mathematics previous year-GATE 2025 Equivalence relation Let R and S be any two equivalence.<\/p>\n

[fvplayer id=”232″]<\/p>\n

It looks like you are looking for Discrete Mathematics \u2013 Equivalence Relations \u2013 Previous Year GATE Questions<\/strong> related to GATE 2025<\/strong>. Here\u2019s a conceptual breakdown along with a sample problem:<\/p>\n

\u00a0Equivalence Relation \u2013 Definition<\/strong><\/h3>\n

A relation R<\/strong> on a set S<\/strong> is called an Equivalence Relation<\/strong> if it satisfies the following three properties:<\/p>\n

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  1. Reflexive<\/strong>: aRaaRa<\/span>a<\/span>R<\/span>a<\/span><\/span><\/span><\/span> for all a\u2208Sa \\in S<\/span>a<\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>.<\/li>\n
  2. Symmetric<\/strong>: If aRbaRb<\/span>a<\/span>R<\/span>b<\/span><\/span><\/span><\/span>, then bRabRa<\/span>b<\/span>R<\/span>a<\/span><\/span><\/span><\/span> for all a,b\u2208Sa, b \\in S<\/span>a<\/span>,<\/span>b<\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>.<\/li>\n
  3. Transitive<\/strong>: If aRbaRb<\/span>a<\/span>R<\/span>b<\/span><\/span><\/span><\/span> and bRcbRc<\/span>b<\/span>R<\/span>c<\/span><\/span><\/span><\/span>, then aRcaRc<\/span>a<\/span>R<\/span>c<\/span><\/span><\/span><\/span> for all a,b,c\u2208Sa, b, c \\in S<\/span>a<\/span>,<\/span>b<\/span>,<\/span>c<\/span>\u2208<\/span><\/span>S<\/span><\/span><\/span><\/span>.<\/li>\n<\/ol>\n

    \u00a0Example GATE Question on Equivalence Relations<\/strong><\/h3>\n

    Question:<\/strong>
    Let R<\/strong> and S<\/strong> be two equivalence relations on a set AA<\/span>A<\/span><\/span><\/span><\/span>. Consider the relation R\u2229SR \\cap S<\/span>R<\/span>\u2229<\/span><\/span>S<\/span><\/span><\/span><\/span> (intersection of R and S). Is R\u2229SR \\cap S<\/span>R<\/span>\u2229<\/span><\/span>S<\/span><\/span><\/span><\/span> also an equivalence relation?<\/p>\n

    Solution Approach:<\/strong><\/p>\n