JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank Self Evaluation Test - Mathematical Reasoning

  • question_answer
    The statement \[p\to (q\to p)\]is equivalent to

    A) \[p\to (p\to q)\]

    B) \[p\to (p\vee q)\]

    C) \[p\to (p\wedge q)\]

    D) \[p\to (p\leftrightarrow q)\]

    Correct Answer: D

    Solution :

    [d] Let us make the truth table for the given statements, as follows:
    \[p\] \[q\] \[p\vee q\] \[q\to p\] \[p\to \]\[(q\to p)\] \[p\to \]\[(p\vee q)\]
    T T T T T T
    T F T T T T
    F T T F T T
    F F F T T T
    From table we observe \[p\to (q\to p)\] is equivalent to \[p\to (p\vee q)\]


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