JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank Mathematical Logic

  • question_answer
    The propositions \[(p\Rightarrow \ \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a    [Karnataka CET 1997]

    A)                 Tautology and contradiction

    B)                 Neither tautology nor contradiction

    C)                 Contradiction

    D)                 Tautology

    Correct Answer: C

    Solution :

                      
    p ~p pÞ~p ~pÞ p \[(p\Rightarrow \ \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\]
    T F F T F
    F T T F F
                    Clearly, \[(p\Rightarrow \ \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a contradiction.


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