Determine whether the following arguments are valid or invalid. Use any method you wish to practice.

1. A v H, ~H ( L v G ), ( G & B ) v [ G & ( K G ) ] / A

2. [( E G ) ~H ], ~H / ~E v ~G

3. ~R ~( K K ), ( R v M ) N / N

4. Z ( S v G ), Z & ( U G ) / S & U

5. ( A v ~B ) v ~C, ( D v G ) v C / ~A [ B ( G v D ) ]

6. A C, A v C / A & C

7. B ( C & D ), ~E v ~H, E ( B v G ), G ( D H ) / G v ~E

8. ~( A & B ), ( ~A C ), ( ~B D ) / C & D

9. ( O P ) R, ~R / ~O v P

10. B ( E G ), A ( C D ), A v B, ~D & ~G / ~C v ~E

11. X v ( C & A ), ~Y v ~B, ~Y v ( ~X & W ), W ( A B ) / W & ~Y

12. ~( Z A ), Z B, ~A C / C & ~B

13. M & L, [ L & ( M & ~S ) ] K, ~K v ~S, ~( K ~S ) / ~L & ~M

14. ( R v S ) T, ( P v Q ) T, R v P / T

15. ~( D E ), ~D H, E G / H & G

16. ( A B ) & ( A C ) / A ( B v C )

17. ( H v ~S ) & ( H  Z ), ~S P / P Z

18. ~[( J & K )  ( M v N )] / K & N

19. ~E ( G & A ), ~[( P ~L ) v E ], ~( P & L ) v Q, ~N ~G / Q & A

20. A [ ( ~N v N ) ( S v T ) ], T ~( F v ~F ) / A S

21. C B, ( ~C A ) v E, D & ~E, B ( A & ~B ) / ( A & ~B ) v A

22. ( R & S ) ( G & H ), R S, H G / R H

23. ( G E ) S, S v ~H, ~( E & ~H ) / G & E

24. ( ~C v ~R ) & ( R L ), C ( C v L ), J R / ~J

25. ~[( C ~D ) v E ], ~E ( G & H ), ( C & D ) K, ~N ~G / K & H

Answers