Philosophy 251: Handout #9

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

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

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

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

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

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