JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

  • question_answer
    Let \[\operatorname{R}=\{(3,3),(5,5),(9,9)(12,12),\] \[(5,12),(3,9),(3,12)(3,5),\}\] be a relation on the set A = {3, 5, 9, 12} . Then, R is :     JEE Main  Online Paper (Held On 22 April 2013)

    A)  reflexive, symmetric but not transitive.

    B)  symmetric, transitive but not reflexive

    C)  an equivalence relation.

    D)  reflexive, transitive but not symmetric

    Correct Answer: D

    Solution :

     Let R \[=\{(3,3),(5,5),(9,9),(12,12),(5,12),\]\[(3,9),(3,12),(3,5)\}\]be a relation on set \[A=\{3,5,9,12\}\] Clearly, every element of A is related to itself. Therefore, it is a reflexive. Now, R is not symmetry because 3 is related to 5 but 5 is not related to 3. Also R is transitive relation because it satisfies the property that if \[a\text{ }R\text{ }b\] and \[b\text{ }R\text{ }c\]then\[a\,R\,c.\]

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