Introductory Logic Quiz #4 October 10, 2005 Name: ________________________ R. Hammack Score: _________

1.
Translate the following sentences into symbolic form.
 (a) If pharmaceutical makers conceal test results, they are subject to substantial fines.

P ⊃ S

Where
P = pharmaceutical makers conceal test results,
S = they are subject to substantial fines

 (b) Three-strikes laws will be enforced and longer sentences imposed only if hundreds of new prisons are built, and that will happen only if taxes are increased.

[(S • L) ⊃ H] • (H ⊃ I)

Where
S = Three-strikes laws will be enforced
L = longer sentences (will be) imposed
H= hundreds of new prisons are built
I = taxes are increased

2.

 (a) Write out the truth table for ⊃

 p q
p ⊃ q
 T T T F F T F F
 T F T T

 (b) Write out the truth table for •

 p q
p • q
 T T T F F T F F
 T F F F

3. Suppose statements A and B are true, and X and Y are false. Decide if the following statement is true or false.

 X ≡ [(A • ~B) ⊃ (X ∨ A)]

 X ≡ [( A • ~ B ) ⊃ ( X ∨ A )] F F T F F T T T F T T

Statement is FALSE