JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

  • question_answer
    The statement \[p\to (q\to p)\] is equivalent to:     JEE Main  Online Paper (Held On 22 April 2013)

    A)  \[\operatorname{p}\to \operatorname{q}\]                

    B)  \[\operatorname{p}\left( \operatorname{p}\,\vee \operatorname{q} \right)\]

    C)  \[\operatorname{p}\to \left( \operatorname{p}\to \operatorname{q} \right)\]   

    D)  \[\operatorname{p}\to \left( \operatorname{p}\wedge \operatorname{q} \right)\]

    Correct Answer: B

    Solution :

     
    \[q\] \[p\] \[q\to p\] \[p\to (q\to p)\] \[p\vee q\] \[p\to (p\vee q)\]
    T T T T T T
    T F F T T T
    F T T T T T
    F F T T F F
    Since truth value of \[p\to (q\to p)\]and \[p\to (p\vee q)\]are same, hence \[p\to (q\to p)\]is equivalent to \[p\to (p\vee q).\]


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