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

  • question_answer
    Which of the following is a contradiction?

    A) \[(p\wedge q)\wedge \tilde{\ }(p\vee q)\]

    B) \[p\vee (-p\wedge q)\]

    C) \[(p\Rightarrow q)\Rightarrow p\]

    D) None of these

    Correct Answer: A

    Solution :

    [a]
    \[p\] \[q\] \[p\wedge q\] \[p\vee q\] \[\tilde{\ }(p\vee q)\] \[(p\wedge q)\wedge \]\[\tilde{\ }(p\vee q)\]
    T T T T F F
    T F F T F F
    F T F T F F
    F F F F T F
    \[\therefore (p\wedge q)\wedge (\tilde{\ }(p\vee q))\] is a contradiction.


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