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# Translate the following sentence into propositional form.

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1. Translate the following sentence into propositional form. Use the letters suggested for affirmative statements.

We'll go to the park if today is Saturday and it's not raining. (P. S, R)

2. Translate the following sentence into propositional form. Use the letters suggested for affirmative statements.

Neither Alexander Hamilton nor Ethan Allen were American presidents. (A, E)

3. Determine if the following is a Well Formed Formula.

~(~A v X) > (W = ~Q)

4. If A, B, and C are TRUE and X, Y, and Z are FALSE and P and Q are UNDETERMINED what is the truth value of the following proposition?

~A v (~P . Q)

5. If A, B, and C are TRUE and X, Y, and Z are FALSE and P and Q are UNDETERMINED what is the truth value of the following proposition?

(~X v ~Q) > (P > C)

6. If A, B, and C are TRUE and X, Y, and Z are FALSE and P and Q are UNDETERMINED what is the truth value of the following proposition?

(~C . ~Q) = (~Y v P)

7. Use truth tables to determine whether the following propositions are logically equivalent, contradictory, consistent, or inconsistent.

~X = Y

(~X > Y) . (Y > ~X)

8. Construct a truth table to determine whether the following proposition is tautologous, self-contradictory, or contingent.

[(A > D) > D] > A

9. Construct an indirect truth table to determine whether the following argument is valid or invalid.

P > (Q v R) / R > (T . S) / ~Q // P > ~S

10. Construct an indirect truth table to determine whether the following statements are consistent or inconsistent.

X = (R . ~Z) / R > (Z . S) / S > ~X / R . ~X

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