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

  • question_answer
    Which of the following is always true?

    A) \[(\tilde{\ }p\Rightarrow q)=\tilde{\ }q\Rightarrow \tilde{\ }p\]

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

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

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

    Correct Answer: C

    Solution :

    [c] \[p\Rightarrow q\equiv \tilde{\ }p\vee q\therefore \tilde{\ }(p\Rightarrow q)\equiv p\wedge \tilde{\ }q.\]


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