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

  • question_answer
    Which of the following is a statement?

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

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

    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] lf \[p\Rightarrow q\equiv \,\sim p\vee q\] \[\sim (p\Rightarrow q)\equiv p\vee \sim q\] It means \[p\Leftrightarrow q\equiv (p\Rightarrow q)\wedge (q\Rightarrow p)\]

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