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

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~ 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 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 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)