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Math Help - logic prove

  1. #1
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    logic prove

    Use basic equivalences to prove:

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  2. #2
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    Hello, theory07!

    Use basic equivalences to prove: . \left[(q \to p) \wedge (r \vee\:\sim q)\right] \;\equiv \; \left[q \to (p \wedge r)\right]

    On the left we have: . (\underbrace{q \to p}) \wedge ( r \:\vee \:\sim q )

    . . . . . . . . . . . . . . . (\sim q \vee p) \wedge \underbrace{(r\: \vee \sim q)}

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

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

    . . . . . . . . . . . . . . . . . q \to (p \wedge r)


    I'll let you supply the reasons . . .

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