Philosophy 251: Handout #6

X. Determine the truth value of each of the following formulas, given that the truth values of the atomic formulas are as follows--P = F, Q = T, R = T.

1. ~[~P v ( ~ Q v ~R )]	6. ~[ P v ( ~Q & ~R )]
2. ( P Q ) v ( Q R )	7. ( P Q ) ( Q R )
3. ( P Q ) v ( Q R )	8. ~P ( Q R )
4. ~[ R ( P v Q ) ] & ~~R	9. ~[~P ~( R ~ [ P ( Q & R )])]
5. ~( R ~P ) & [ Q ( P & R )]	10. ~ [~( P ~Q ) ~P ] ( Q v R )

XI. Construct complete truth tables for each of the following formulas. For each formula determine whether the formula is contingent, a tautology, or a contradiction.

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

XII. For each of the following pairs of formulas determine whether imples , implies , or whether and are logically equivalent.

1. ~( A & B )	~( A v B )	4. C ( D C )	( C & ~C ) v ( E E )
2. X ( ~X X )	~ ( X ~X )	5. ~( O & P ) ( P ~R )	( O & P ) ~R
3. ( Q & ~U ) v S	Q v ~ ( ~S & U)

XIII. For each of the following arguments, construct a truth table to determine whether the argument is valid or invalid.

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