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

  • question_answer
    Let p, q and r be any three logical statements. Which of the following is true?

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

    B) \[\tilde{\ }[(p\vee q)\wedge (\tilde{\ }r)\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\vee (\tilde{\ }r)\]

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

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

    Correct Answer: C

    Solution :

    [c] Statement given in option [c] is correct. \[\tilde{\ }[p\vee (\tilde{\ }q)]=(\tilde{\ }p)\wedge \tilde{\ }(\tilde{\ }q)=(\tilde{\ }p)\wedge q\]


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