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

  • question_answer
    The contrapositive of \[(p\vee q)\Rightarrow r\] is          [Karnataka CET 1999]

    A)                 \[r\Rightarrow (p\vee q)\]         

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

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

    D)                 \[p\Rightarrow (q\vee r)\]

    Correct Answer: C

    Solution :

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


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