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

  • question_answer
    \[\tilde{\ }(p\Rightarrow q)\Leftrightarrow \tilde{\ }p\vee \tilde{\ }q\] is

    A) A tautology

    B) A contradiction

    C) Neither a tautology nor a contradiction

    D) Cannot come to any conclusion

    Correct Answer: C

    Solution :

    [c]
    \[p\] \[q\] \[p\Rightarrow q\] \[\tilde{\ }(p\Rightarrow q)\] \[\tilde{\ }p\] \[\tilde{\ }q\] \[\tilde{\ }p\vee \tilde{\ }q\] \[\tilde{\ }(p\Rightarrow q)\]\[\Leftrightarrow \tilde{\ }\]\[p\vee \tilde{\ }q\]
    T T T F F F F T
    T F F T F T T T
    F T T F T F T F
    F F T F T T T F
    Last column shows that result is neither a tautology nor a contradiction.


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