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JEE Main & Advanced AIEEE Solved Paper-2005

  • question_answer
    Let\[R=\{(3,3),(6,6),(9,9),(12,12),\]\[(6,12),\]\[(3,9),(3,12),(3,6)\}\]be a relation on the set A\[=\{3,6,9,12\}\]. The relation is     AIEEE  Solved  Paper-2005

    A) reflexive and symmetric only

    B) an equivalence relation

    C) reflexive only

    D) reflexive and transitive only

    Correct Answer: D

    Solution :

    Since, (3, 3), (6, 6), (9, 9), (12, 12) \[\in R\] \[\Rightarrow \]R is reflexive relation. Now,\[(6,12)\in R\]but\[(12,\text{ }6)R,\]so it is not a symmetric relation. Also, \[(3,6),(6,12)\in R\] \[\Rightarrow \]\[(3,12)\in R\] \[\Rightarrow \]R is transitive relation. Note Any relation is said to be an equivalence relation, if it is reflexive, symmetric and transitive relations simultaneously.


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