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

  • question_answer
    If p, q, r are simple propositions with truth values T, F, T, then the truth value of \[(\tilde{\ }p\vee q)\ \wedge \tilde{\ }r\Rightarrow p\] is

    A)                 True      

    B)                 False

    C)                 True if r is false 

    D)                 True if q is true

    Correct Answer: A

    Solution :

                       \[\tilde{\ }p\vee q\] means F\[\vee \]F = F, ~r means F\[(\tilde{\ }p\vee q)\wedge \tilde{\ }r\] means F                    \[\because \]\[[(\tilde{\ }p\vee q)\ \wedge \tilde{\ }r]\Rightarrow p\] means T                                 [\[\because \] in \[p\Rightarrow q\] we have FTT]


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