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

  • question_answer
    The Boolean Expression \[(p\wedge \tilde{\ }q)\vee q\vee (\tilde{\ }p\wedge q)\]is equivalent to

    A) \[p\wedge q\]     

    B) \[p\vee q\]

    C) \[p\,\vee \tilde{\ }q\]       

    D) \[\tilde{\ }p\wedge q\]

    Correct Answer: B

    Solution :

    [b] \[[(p\wedge \sim q)\vee q]\vee (\sim p\wedge q)\] =\[(p\vee q)\wedge (\sim q\vee q)\vee (\sim p\wedge q)\] \[=(p\vee q)\wedge [t\vee (\sim p\wedge q)]\] \[=(p\vee q)\wedge t\] \[=p\vee q\]

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