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Math Help - Predicates help

  1. #1
    Junior Member
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    Predicates help

    a)
    Determine whether (p →q) ^ (p → q) ≡q.

    b)
    Find a proposition with three variables p, q, and r that is true when p and r are true and q is false, and false otherwise.
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  2. #2
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    Hello, captainjapan!

    a) Determine whether: . [(p \to q) \wedge  (\sim p \to q)] \:\Longrightarrow \:q

    By propositional logic . . . you can supply the reasons:


    (p \to q) \wedge ( \sim p \to q)

    (\sim p \vee q) \wedge (p \vee q)

    (\sim p \wedge p) \vee q

    f \vee q

    q



    By truth table . . .

    . . . \begin{array}{|c|c|| ccccccccc|}<br />
p & q & [(p & \to & q) & \wedge & (\sim p & \to & q)] & \to & q \\ \hline \hline<br />
T & T & T & T & T & T & F & T & T & {\color{blue}T} & T \\<br />
T & F & T & F & F & F & F & T & F & {\color{blue}T} & F \\<br />
F & T & F & T & T & T & T & T & T & {\color{blue}T} & T \\<br />
F & F & F & T & F & F & T & F & F & {\color{blue}T} & F \\ \hline<br />
& & 1 & 2 & 1 & 3 & 1 & 2 & 1 & 4 & 1 \end{array}

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