Philosophy 251: Handout #10

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

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

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