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

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    \[(p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] is                                           [Karnataka CET 2003]

    A)                 A tautology

    B)                 A contradiction

    C)                 Both a tautology and a contradiction

    D)                 Neither a tautology nor a contradiction

    Correct Answer: B

    Solution :

                       \[(p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)=(p\ \wedge \tilde{\ }p)\wedge (\tilde{\ }q\wedge q)=f\wedge f=f\].                    (By using associative laws and commutatine laws)                                 \ \[(p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] is a contradiction.


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