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

  • question_answer
    Consider the following statements
    P: Suman is brilliant
    Q: Suman is rich
    R: Suman is honest
    The negation of the statement "Suman is brilliant  and dishonest if any only if suman is rich" can be expressed as

    A) \[\tilde{\ }(P\wedge \tilde{\ }R)\leftrightarrow Q\]

    B) \[\tilde{\ }(P\wedge (Q\leftrightarrow \,\tilde{\ }R)\]

    C) \[\tilde{\ }(Q\leftrightarrow (P\wedge \tilde{\ }R))\]

    D) \[\tilde{\ }Q\leftrightarrow \,\tilde{\ }P\wedge R\]

    Correct Answer: C

    Solution :

    [c] Suman is brilliant and dishonest is \[P\wedge \sim R\] Suman is brilliant and dishonest iff Suman is rich is \[Q\leftrightarrow (P\wedge \sim R)\] Negative of statement is expressed as \[\sim (Q\leftrightarrow (P\wedge \sim R)\]

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