JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    If R & R' are symmetric relation (not disjoint) on a set A, then the relation \[R\cap R'\] is

    A)  reflexive                            

    B)  symmetric

    C)  transitive                           

    D)  equivalence

    Correct Answer: B

    Solution :

    As R & R' are not disjoint, there is atleast one ordered pair say (a,b) in\[R\cap R'.\] But \[(a,b)\in R\cap R'\Rightarrow (a,b)\in R\And (a,b)\in R'\] As RR' are symmetric so \[(a,b)\in R(b,a)\in R'\] \[\therefore \]\[(b,a)\in R\cap R'\] Hence \[R\cap R'\]is symmetric.

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