JEE Main & Advanced Sample Paper JEE Main Sample Paper-5

  • question_answer
    If p, q and r are false statements, then which among the following is false?

    A)  \[\tilde{\ }q\vee r\] is true            

    B)  \[\tilde{\ }r\vee q\]is true

    C)  \[\tilde{\ }(q\vee r)\wedge (\tilde{\ }r\,\vee q)\]is false                         

    D)  \[p\wedge [\tilde{\ }q\vee r)\wedge (\tilde{\ }r\,\vee q)]\]is false

    Correct Answer: C

    Solution :

    Let, \[s:p\wedge [(\tilde{\ }q\vee r)\wedge (\tilde{\ }r\vee q)]\]
    \[p\] \[q\] \[r\] \[\tilde{\ }q\] \[\tilde{\ }r\] \[\tilde{\ }q\vee r\] \[\tilde{\ }r\vee q\] \[(\tilde{\ }r\vee r)\vee \]\[\wedge (\tilde{\ }r\vee q)\] \[s\]
    F F F T T T T T F
    As per the truth table given above, it is clear that s has truth value F and only option  is false since \[(\tilde{\ }q\vee r)\wedge (\tilde{\ }r\vee q)\]is true T

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