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Thread: 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: .$\displaystyle \left[(q \to p) \wedge (r \vee\:\sim q)\right] \;\equiv \; \left[q \to (p \wedge r)\right] $

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

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

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

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

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


    I'll let you supply the reasons . . .

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