Question 1

Translate each statement into propositional logic form.
-If Ike is a baby, then Stan will kick him.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-If...

Question 2

Translate each statement into propositional logic form.
-Either Damian or Mr. Hankey killed Kenny.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-Either...

Question 3

Translate each statement into propositional logic form.
-Cartman is not fat, but he does have big bones.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-Cartman...

Question 4

Translate each statement into propositional logic form.
-If Pip is English, then either Damian is not Satan's son or Mr. Garrison is not a good teacher.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-If...

Question 5

Translate each statement into propositional logic form.
-Either Stewie is a megalomaniac, or Lois is crazy.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-Either...

Question 6

Translate each statement into propositional logic form.
-If Mel Gibson is a masochist, then Stan and Kyle should get their money back.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-If...

Question 7

Translate each statement into propositional logic form.
-Homer eats donuts if and only if donuts exist.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-Homer...

Question 8

Translate each statement into propositional logic form.
-If Patrick Stewart made an appearance, then either Stewie or Peter said "Wil Wheaton" strangely.

Accepted Answer

The answer of Translate each statement into propositional logic form.
-If...

Question 9

Given that A, B, and C are true and X, Y, and Z are false, determine the truth- value of the following statements.
-A v (B ? Z)

Accepted Answer

The symbol "?" is not a standard logical operator, but assuming it's meant to be a placeholder for a standard operator, the truth value of "A v (B ? Z)" depends primarily on "A" since "A v anything" will be true if "A" is true, regardless of the other components.

Question 10

Given that A, B, and C are true and X, Y, and Z are false, determine the truth- value of the following statements.
-~B v ~X

Accepted Answer

Since X is false, ~X (not X) is true. The statement "~B v ~X" uses the logical OR operator (v), which means the statement is true if at least one of the operands is true. Since ~X is true, the entire statement is true regardless of ~B's truth value.

Question 11

Given that A, B, and C are true and X, Y, and Z are false, determine the truth- value of the following statements.
-(X & A) & (~B & Y)

Accepted Answer

The statement (~B & Y) is false because ~B is false (since B is true) and Y is false, making the whole expression false.

Question 12

Given that A, B, and C are true and X, Y, and Z are false, determine the truth- value of the following statements.
-[(A v B) & ~(Y & ~C)] v ~[~(Z ? ~X) v ~B]

Accepted Answer

The statement simplifies as follows: [(A v B) & ~(Y & ~C)] v ~[~(Z ? ~X) v ~B] simplifies to True because:- (A v B) is True since both A and B are true.- ~(Y & ~C) is True because Y is false and ~C is false, making Y & ~C false, and its negation (~) true.- Thus, the left side of the main disjunction [(A v B) & ~(Y & ~C)] is True.- For the right side, Z ? ~X is not a standard logical operator, but assuming it's meant to be a placeholder for a logical operation (like AND, OR, etc.), the outcome of [~(Z ? ~X) v ~B] depends on the operation. However, since Z is false and X is false, most standard operations would result in a false or true value that, when negated, would not affect the overall truth because ~B is false, making [~(Z ? ~X) v ~B] false, and its negation (~) true.- Therefore, the entire expression simplifies to True v True, which is True.

Question 13

Given that A, B, and C are true and X, Y, and Z are false, determine the truth- value of the following statements.
-~{~[~(A ? ~Y) & ~(Y ? C)] v ~[~(B ? ~Z) & ~(X v A)]}

Accepted Answer

The given expression simplifies to false because the inner expressions evaluate to true, making the negations false, and the disjunction of false values is false.

Question 14

Construct truth tables for the following arguments and indicate their validity.
-$ \begin{array}{l}\mathrm{A} \rightarrow \sim \mathrm{B} \ \end{array} $

$\frac {\text { B }} { \text { ?A} }$

Accepted Answer