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show that [(p =>q)v(p=>q)] and p => (q v r) are logical equivalent Solution 1. ~

ID: 3651536 • Letter: S

Question

show that [(p =>q)v(p=>q)] and p => (q v r) are logical equivalent

Explanation / Answer

1. ~P > (Q & ~Q) Premise 2. ~~P v (Q & ~Q) 1 Material Implication 3. P v (Q & ~Q) 2 Double Negation 4. (P v Q) & (P v ~Q) 3 Distribution 5. P v Q 4 Simplification 6. (P v ~Q) & (P v Q) 4 Commutation 7. P v ~Q 6 Simplification 8. ~Q v P 7 Commutation 9. ~~P v Q 5 Double Negation 10. ~P > Q 9 Material Implication 11. Q > P 8 Material Implication 12. ~P > P 10,11 Hypothetical Syllogism 13. ~~P v P 12 Material Implication 14. P v P 13 Double Negation 15. P 14 Tautology

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