Philosophy 251: Handout #10

XVIII. For each of the following arguments construct a derivation to prove that the argument is valid.

1. ( P & Q ) R / [ ( P Q ) P ] [ ( P Q ) R ]
2. ( ~P & Q ) R / ( ~Q P ) ( ~P R )
3. P v Q, P R, Q v ~R / Q
4. ( P v ~Q ) ( R & ~S ), Q v S / Q
5. / ~~[( A v A ) & B ] v ( A ~B )
6. F ( G H ), ~I ( F v H ), ( ~H ~G ) I / I v H
7. / [ ( A v B ) C ] [ ( A C ) & ( B C ) ]
8. L ( C v T ), ( ~L v B ) & ( ~B v ~C ) / L T
9. A v B, ~( A & B ) / ( A B ) ~( B A )
10. ( C & A ) v ( B & C ), ~D ~ ( B v A ) / D
11. / [ ( A v B ) v ~ B ] v ~ A
12. C ~C, ~C ( R T ) / ( T & T ) v ~R
13. / ( A B ) v ( B A )
14. ~( R v W ), ( R M ) v [ ( M v G ) ( W M ) ] / ~M
15. P v Q, P v R, Q v R / ( P & Q ) v [ ( P & R ) v ( Q & R ) ]
16. ( A & B ) v ( A & C ) / A
17. D v ( E F ), ~F, E / D
18. ( M N ), ( N ~L ) / ~( M L )
19. J v K, ~K ( L v M ), ( M & N ) v [ M & ( O  M )] / J
20. ( P v Q ) v ( R & S ), ( P T ) & ( Q  U ), W ~( T v U ), R  Q / ~W