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

  • question_answer
    The following statement \[(p\to q)\to [(\tilde{\ }p\to q)\to q]\]is

    A) a fallacy

    B) a tautology

    C) equivalent to \[\tilde{\ }p\to q\]

    D) equivalent to \[p\to \tilde{\ }q\]

    Correct Answer: D

    Solution :

    [d] \[\tilde{\ }s\vee (\tilde{\ }r\wedge s)=(\tilde{\ }s\vee \tilde{\ }r)\wedge (\tilde{\ }s\vee s)\] \[=\tilde{\ }(\tilde{\ }s\wedge r)\wedge t\] \[=\tilde{\ }(s\wedge r)\] So, negation is \[s\wedge r\].

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