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Question Number 198750 by depressiveshrek last updated on 24/Oct/23

$$\mathrm{Prove}\mathrm{the}\mathrm{following}\mathrm{is}\mathrm{a}\mathrm{tautology}:$$$$[(p⊻q)\wedge (p\Rightarrow r)]\Rightarrow (q⊻r)$$

Answered by MathematicalUser2357 last updated on 29/Dec/23

$$\mathrm{Only}\mathrm{know}\mathrm{until}$$$$=\sim [(p⊻q)\wedge (\sim p\vee r)]\vee (q⊻r)$$$$=\left(p\stackrel{-}{⊻}q\right)\vee p\wedge \sim r\vee (q⊻r)$$$$=\sim p\wedge \sim q\vee p\wedge q\vee p\wedge \sim r\vee \sim p\wedge r$$$$=p\vee q\vee r\wedge (\sim p\vee \sim r)$$

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