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

  • question_answer
    The statement \[p\to (p\to q)\]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: B

    Solution :

    [b] \[p\to (q\to p)=-p(q\to p)\] \[=\sim p\vee (\sim q\vee p)\] (Since\[p\vee \sim p\]is always true) \[=\sim p\vee p\vee q=p\to (p\vee q)\]

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