Philosophy 251: Handout #8

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

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

XVII. For each of the following arguments construct a truth-tree to determine whether the argument is valid or invalid.

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