Philosophy 251: Handout #11

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

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

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

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