Philosophy 251: Handout #7

XIV. For each of the following arguments use the countermodel method to determine if the argument is valid or invalid. If the argument is invalid, be sure to specify at least one set of truth values that demonstrate the argument is invalid.

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

XV. For each of the following sets construct a truth-tree to determine whether the set is consistent or inconsistent.

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