Philosophy 251: Handout #8

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

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

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

1. V W / ~W ~V
2. O v ~P, ~O v ~P / ~P
3. ( X Y )  Z, ( X Y ) v ~Z / ~Z ~( X Y )
4. E ( ~F v G ), F G / E
5. ~( A B), ~( B C ) / ~D
6. J ( K & L ), ( ~K L ) & ( M  J ) / ( J v L )  ~M
7. ~( N O ) / ~N O
8. / ~[( P & Q ) & ~( P & Q )]
9. / ( V W ) v ( W V )
10. / [( X v Y ) Z ] [( X Z) & ( Y Z )]