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

  • question_answer
    If p and q are two statements, then \[(p\Rightarrow q)\Leftrightarrow (\tilde{\ }q\Rightarrow \tilde{\ }p)\]is a

    A) contradiction     

    B) tautology

    C) neither [a] nor [b]

    D) none of the above

    Correct Answer: B

    Solution :

    \[p\Rightarrow q\] \[\sim p\Rightarrow \sim q\] \[p\Rightarrow q\Leftrightarrow \sim q\Rightarrow \sim p\]
    T T T
    F F T
    T T T
    T T T
    Therefore, it is a tautology Hence, the given proposition is a tautology.

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