CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    \[(p\wedge \,\,\,\,\,\,\,p)\wedge (\sim p\wedge q)\]is:

    A)  a tautology

    B)  a contradiction

    C)  tautology and contradiction

    D)  neither a tautology nor a contradiction

    Correct Answer: B

    Solution :

    Prepare a truth table for given operation
    p q \[\wedge p\] \[\sim p\] \[\wedge p\sim nq\] \[\sim p\wedge q\] \[(p\wedge q)\wedge (\sim p\wedge q)\]
    T T F F F F F
    T F F T T F F
    F T T F F T F
    F F T T F F F
    As we see from the last column of truth table all entries are F. So, \[(p\wedge \sim q)\wedge (\sim p\wedge q)\] is a contradiction.


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