# Translate the following sentence into propositional form.

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

~ tilde

. conjunction

v disjunction

> implication

= biconditional

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

If today is Saturday and it is not raining, then we will play golf. (S,R,G)

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

Class would be cancelled today if it was snowing. (C,S)

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

Mulder believes that the truth is out there but Scully does not. (M,S)

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

Logic is not difficult if and only if you study the material. (L,M)

Question 4 answers

Question 5

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

Neither Brazil nor Argentina are in North America. (B,A)

Question 6

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

~(B v C)> (X = Y)

Question 7

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

A > [A >(A > Z)]

Question 8

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

A . [(X v Y) > (B > ~A)]

Question 9

Determine if the following is a Well Formed Formula.

~~D . (A > B)(X v Y)

Question 9 answers

Question 10

Determine if the following is a Well Formed Formula.

(L v ~Q) . ~(~A = ~B)

Question 11

Determine if the following is a Well Formed Formula.

A . (B > C > E)

Question 12

Determine if the following is a Well Formed Formula.

(L . M) v (G = Q > R)

Question 13

Determine if the following is a Well Formed Formula.

D = [~E . (F v G)]

Question 14

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

P > [P > (P > P)]

Question 15

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

(A v B) . ~[~A > (B v A)]

Question 16

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

[(A > B) . (B > A)] . ~(A = B)

Question 17

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

(S > R) . (S . ~R)

Question 18

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

~A = X

(X . ~A) v (A . ~X)

Question 19

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

R v ~S

S . ~R

Question 20

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

(X > Y) > Q

X > (Q > Y)

Question 21

Construct a truth table to determine whether the following argument is valid or invalid.

A > (N v Q) / ~(N v ~A) // A > Q

Question 22

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

(X v Y) > (A . B) / (~X v ~Y) > E // (~A v ~B) > E

Question 23

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

(Q v K) > C / (C . F) > (N v L) / C > (F . ~L) / Q . ~N

Question 24

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?

B > (Z . ~P)

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