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

  • question_answer
    Let p and q be any two logical statements and \[r:p\to (\tilde{\ }p\vee q).\] If r has a truth value F, then the truth values of p and q are respectively:

    A) F, F

    B) T, T

    C) T, F

    D) F, T

    Correct Answer: C

    Solution :

    [c] \[p\to (\tilde{\ }p\vee q)\] has truth value F. It means \[p\to (\tilde{\ }p\vee q)\] is false. It means p is true and \[\tilde{\ }p\vee q\] is false. \[\Rightarrow p\] is true and both \[\tilde{\ }p\] and q are false. \[\Rightarrow p\] is true and q is false.


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