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Math Help - Truth Tables

  1. #1
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    Truth Tables

    Given the truth table below defined for the operation *, answer the following questions:

    p | q | p*q
    -----------
    T | T | F
    T | F | F
    F | T | T
    F | F | F

    a.) Determine whether * is an associative operation (ie., does (p*q)*r = p*(q*r)? Use the truth table, explain.

    b.) Determine whether * is a distributive operation (ie., does p*(q v r) = (p*q) v (p*r). Use the truth table again.

    c.) Express p*q in terms of p, q, ^, v, ~ (note that not all of them have to be used)

    d.) Express p -> q in terms of p, q, ~, * (no others are used)
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  2. #2
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    c)\quad \left( {p*q} \right) \equiv \left( { \sim p \wedge q} \right)\quad \& \quad d)\quad \left( {p \to q} \right) \equiv  \sim \left( {q*p} \right)<br />

    You must do the others. They are just too tedious.
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