JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank Mock Test - Mathematical Reasoning

  • question_answer
    \[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\] is equivalent to

    A) q                     

    B) p

    C) ~p       

    D) ~q

    Correct Answer: C

    Solution :

    [c] \[\sim (p\vee q)\vee (\sim p\wedge q)\equiv (\sim p\wedge \sim q)\vee (\sim p\wedge q)\]               \[\equiv \sim q\wedge \sim (\sim (p\wedge q))\] \[\equiv \tilde{\ }q(p\wedge q)\]

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