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Question: 7 propositional logic proofs for the following give proofs for...

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7 Propositional logic proofs for the following:

give proofs for the following using any system.

1. Premise: P Conclusion: q v (r -> p)

2. Premise: P Conclusion: (p ->r) <-> r

3. Premise: p v q, p -> r, q -> s Conclusion: r v s

4. Premise: q Conclusion: (~p -> ~q) -> p

5. Premise: p -> (q v r), ~r Conclusion: ~q -> ~p

6. Premise: (p -> q) & (q -> r), ~q v ~r Conclusion: ~p

7. p v q, r -> ~q, ~p, ~p, ~r -> s Conclusion: s
Proofs

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