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    Discrete Math: Logic Problems, Truth Table and Rules of Inference

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    1. Construct the truth table for the compound proposition: [p (q r)] (r p)
    p q r
    T T T
    T T F
    T F T
    T F F
    F T T
    F T F
    F F T
    F F F

    2. What is the negation of the quantified statement:
    For every integer, x, there is an integer, y, such that x + y = 0.

    3. Use the rules of inference to deduce the following conclusion from the following set of premises.
    Premises: p r
    r q
    p s t
    ~r u s
    Conclusion: t

    4. Decide if the following is a Valid Argument and justify your reasoning:
    All movie stars drive fast cars.
    Dan Gordon drives a fast car.
    Therefore, Dan Gordon is a movie star.

    5. Later in this course, we will study the Inclusion-Exclusion Rule:
    |A B C| = |A| + |B| + |C| |A B| |A C| |B C| + |A B C|.
    Verify this for the sets A = {2,3,7,9}, B = {2,3,4}, and C = {1,3,5,7,9}.

    6. Find A B for the sets A = { , {} } and B = { {}, {0} }

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    Solution Summary

    Logic problems are solved for discrete mathematics. The truth tables and rule of inferences are analyzed. The solution is detailed and well presented.