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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relation and Functions-II

  • question_answer
    Let S be any set and P (S) be its power set, We define a relation R on P(S) by ARB to mean \[A\subseteq B;\forall A,B\in P(S).\] Then R is

    A) Equivalence relation

    B) Not an equivalence but partial order relation

    C) Both equivalence and partial order relation

    D) None of these

    Correct Answer: B

    Solution :

    [b] (i)\[A\subseteq Aie,ARA,\forall A\in P(S)\] \[\therefore \] R is reflexive. (ii) \[A\subseteq BB\subseteq A\] \[\therefore ARBBRA\]. So R is not symmetric. (iii) ARB and BRA \[\Rightarrow A\subseteq B\] and \[B\subseteq A\Rightarrow A=B\] Thus, R is anti-symmetric. (iv) ARB and BRC \[\Rightarrow A\subseteq B\,\,and\,\,B\subseteq C\] \[\Rightarrow A\subseteq C\Rightarrow ARC\] \[\therefore \] R is transitive relation. Thus, R is partially ordered relation but not an equivalence relation.


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