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JEE Main & Advanced JEE Main Online Paper (Held on 9 April 2013)

  • question_answer
                    Statement 1: The statement \[\operatorname{A}\to (\operatorname{B}\to \operatorname{A})\] is equivalent to \[\operatorname{A}\to \]\[\left( \text{A}\wedge \text{B} \right).\]                 Statement 2: The statement                 \[\Rightarrow \]\[\tilde{\ }\left[ \left( \text{A}\wedge \text{B} \right)\to \left( \text{ }\!\!\tilde{\ }\!\!\text{ A}\vee \text{B} \right) \right]\] is a Tautology.                   JEE Main Online Paper (Held On 09 April 2013)

    A)                 Statement -1 is false. Statement -2 is true.                

    B) Statement -1 is true, Statement-2 is true. Statement -2 is not correct explanation for statement-1.

    C)                 Statement -1 is true, Statement-2 is true. Statement -2 is correct explanation for statement-1.                

    D)                 Statement -1 is true. Statement-2 is false.                

    Correct Answer: C

    Solution :

                                   
    A B \[A\vee B\] \[B\to A\] \[A\wedge B\] \[\tilde{\ }A\] \[\tilde{\ }A\vee B\] \[A\to \]\[(A\vee B)\]
    T T T T T F T T
    T F T T F F F T
    F T T F F T T T
    F F F T F T T T
    \[A\to (B\to A)\] \[(A\wedge B)\to \]\[(\tilde{\ }A\vee B)\] \[\tilde{\ }[(A\wedge B)\to \]\[(\tilde{\ }A\vee B)]\]
    T T F
    T T F
    T T F
    T T F
    \[\therefore \]  \[A\to (B\to A)\] is equivalent to \[A\to (A\wedge B)\]                 But \[\tilde{\ }[(A\wedge B)\to (\tilde{\ }A\vee B)]\] is not a tautology i.e., it is contradiction.                


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