Philosophy 251: Handout #12

XXV. 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 B ) C ] [ ~( A & B ) v C ]
8. / [ ( A v B ) C ] [ ( A C ) & ( B C ) ]
9. L ( C v T ), ( ~L v B ) & ( ~B v ~C ) / L T
10. A v B, ~( A & B ) / ( A B ) ~( B A )

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

1. ( C & A ) v ( B & C ), ~D ~ ( B v A ) / D
2. / [ ( A v B ) v ~ B ] v ~ A
3. ~( ~P v ~Q ), [ ( T v Q ) & ( P & R ) ] ( T ~T ) / R ~ T
4. / [ ( A B ) & ( B C )] v ( C A )
5. C ~C, ~C ( R T ) / ( T & T ) v ~R
6. / ( A B ) v ( B A )
7. ~( R v W ), ( R M ) v [ ( M v G ) ( W M ) ] / ~M
8. P v Q, P v R, Q v R / ( P & Q ) v [ ( P & R ) v ( Q & R ) ]
9. / ( A ~ A) ~( A ~ A )
10. ( P R ) v ( Q R ) / ( P & Q ) R

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

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