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JEE Main & Advanced Sample Paper JEE Main Sample Paper-9

  • question_answer
    Let N denote the set of all natural numbers and R a relation on \[N\times N.\] Which of the following is an equivalence relation?

    A)  (a, b ) R (c,d) if ad (b + c) = be ( a + d)

    B)  (a, b) R (c, d) if a + d = b + c

    C)  (a,b) R (c,d) if ad = bc

    D)  All the above

    Correct Answer: D

    Solution :

    The relation in [A] is reflexive because ab = ba and a + b = b + a, so that ab (b + a) = ba (a + b ). i.e. (a, b) R(a, b). It is also symmetric because ad(b + c) = bc(a + d), i.e. (a,b) R(a, d).                                     Implies cd (d + a) = da(c + b),i.e,., (c, d) R ,(a, b). Simple computations show that relation  is TRANSITIVE, too, and that the relations in  and  are also reflexive, symmetric and transitive.


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