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I need help with all of these I am confused Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the

I need help with all of these I am confused

Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises.

1. F(GH), ~FJ, ~(GH) J

2. PQ , R~S, P v R, (Q v ~S)(~T v ~W), ~~T ~W

3. (A v G)K, K(BF), AB F

4. ~C(FC), ~C ~F

5. ~(CD), ~CS, ~DT S v T

6. (WU)~X ~U~W

7. ~~T v ~R, ~(S v ~R), (T~S)~Q , WQ ~W

8. ~(JL), (~J v ~L)~M, ~E v (M v ~S) ~(SE)

9. (BA)C, ~BD, ~D C

10. ~(ON), (~OS)(~NT) S v T

11. ~M v N ~N~M

12. ~BC, ~B C

13. (Z v ~Y)(Z v W), Z~~U, ~Y(WU) U

14. ~U~B, S~B, ~(U~S), T v B T

15. AB, BC ~A v C

Use Conditional Proofs (CP) to show that each of the following symbolic arguments are valid. Commas mark the breaks between premises.

16. P(QR) Q(PR)

17. PQ P(Q v R)

18. (BD)(CR), D BR

19. (Z~W)(XU), Z(WY) Z(~YU)

20. (EF)G, A[(B v C)(DE)] A(CG)

Use Reductio ad Absurdum Proofs (RAA) to show that each of the following symbolic arguments are valid. Commas mark the breaks between premises.

21. AB ~(A~B)

22. PQ , ~PJ, ~Q~J Q

23. M(NO), ~NP, (MP)(O v ~Q) ~O~Q

24. (D v E)(FG), (~G v H) (DF) G

25. (ZY)(WX), ZY, XW ZX

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