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JEE Main & Advanced AIEEE Solved Paper-2009

  • question_answer
    Directions: Questions No. 88 are Assertion - Reason type questions. Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Each of these questions also have four alternative choices, only one of which is the correct answer. You have to select the correct choice.   Statement 1:\[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is equivalent to\[p\leftrightarrow q\] Statement 2:\[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is a tautology     AIEEE  Solved  Paper-2009

    A) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement-1

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

    C) Statement-1 is true, statement-2 is false.

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

    Correct Answer: C

    Solution :

    p q ~q \[(p\leftrightarrow \tilde{\ }q)\] \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\] \[p\leftrightarrow q\]
    T T F F T T
    T F T T F F
    F T F T F F
    F F T F T T
    Clearly,\[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is not a tautology because it does not contain T in the column of its truth table. Also,\[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]& \[p\leftrightarrow q\]have the same truth value.


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