JEE Main & Advanced JEE Main Solved Paper-2014

  • question_answer
    The statement \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\] is:   JEE Main  Solved  Paper-2014

    A) equivalent to \[p\leftrightarrow q\]

    B) equivalent to \[\tilde{\ }p\leftrightarrow q\]

    C) a tautology                        

    D) a fallacy

    Correct Answer: A

    Solution :

    Truth table for \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is
          (1) (2) (3)  
    \[p\] \[q\] \[\tilde{\ }q\] \[p\to \tilde{\ }q\] \[\tilde{\ }q\to p\] \[(1)\wedge (2)\] \[\tilde{\ }(3)\]
    \[T\] \[T\] \[F\] \[F\] \[T\] \[F\] \[T\]
    \[T\] \[F\] \[T\] \[T\] \[T\] \[T\] \[F\]
    \[F\] \[F\] \[T\] \[T\] \[F\] \[F\] \[T\]
    Thus \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is equivalent to \[p\leftrightarrow q.\]

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