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