JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank Mathematical Logic

  • question_answer
    The inverse of the proposition \[(p\ \wedge \tilde{\ }q)\Rightarrow r\] is

    A)                 \[\tilde{\ }r\Rightarrow \ \tilde{\ }p\vee q\]       

    B)                 \[\tilde{\ }p\vee q\Rightarrow \ \tilde{\ }r\]

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

    D)                 None of these

    Correct Answer: B

    Solution :

                       Inverse of \[p\Rightarrow q\] is \[\tilde{\ }p\Rightarrow \ \tilde{\ }q\]                    \ inverse of \[(p\ \wedge \tilde{\ }q)\Rightarrow r\] is                 \[\tilde{\ }(p\ \wedge \tilde{\ }q)\Rightarrow \ \tilde{\ }r\] i.e. \[(\tilde{\ }p\vee q)\Rightarrow \ \tilde{\ }r\].


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