logic prove

**theory07** · November 28th 2007, 08:11 AM

Use basic equivalences to prove:

**Soroban** · November 28th 2007, 08:55 AM

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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