Question 1

A statement that is in at least one row is contingent.

Accepted Answer

A) True 
 B)False

Question 2

Using a truth table, we can tell that an argument is valid if

Accepted Answer

A)  there is at least one row where the premises and conclusion are all true. 
B)  there is no row where the premises are true and the conclusion is false. 
C)  there is no row where the conclusion is false. 
D)  there is at least one row where the premises are all true and the conclusion is false.

Question 3

Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\
Translate the following statement into symbols, using the schemes of abbreviation provided: It will snow
if and only if it is below 32° out and the humidity is greater than 60 percent. (S: It will snow; B: It is
below 32° out; H: The humidity is greater than 60 percent.)

Accepted Answer

The answer of Symbols list
You may use the list below...

Question 4

A statement that is false regardless of the truth values assigned to the atomic statements that compose it is a contradiction.

Accepted Answer

A) True 
 B)False

Question 5

Symbols list You may use the list below to copy-and-paste the symbols into your answer as needed. →;↔;•;~;⋁;\ Translate the following statement into symbols, using the schemes of abbreviation provided: The presence of H₂O on Mars is sufficient for the production of life-forms. (H: H₂O is present on Mars; P: Life-forms are produced on Mars.)

Accepted Answer

The answer of Symbols list
You may use the list below...

Question 6

"Chocolate is not nutritious" is an atomic statement.

Accepted Answer

A) True 
 B)False

Question 7

In (A ⋁ B) → [B • (C ⋁ ~D)], what is the main logical operator?

Accepted Answer

A)  the first occurrence of ⋁ B. • 
C)  → 
D)  the second occurrence of ⋁

Question 8

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: A ↔ (C ⋁ D)

Accepted Answer

A) True 
 B)False

Question 9

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: B → ~(A • B)

Accepted Answer

A) True 
 B)False

Question 10

Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true?

Accepted Answer

A)  A is true, B is false, and C is false. 
B)  A is false, B is true, and C is false. 
C)  A is false, B is false, and C is false. 
D)  A is true, B is false, and C is true.

Question 11

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: (A • B) → (A ⋁ ~(C ⋁ B))

Accepted Answer

A) True 
 B)False

Question 12

The statement ~A ⋁ B is a negation.

Accepted Answer

A) True 
 B)False

Question 13

The English phrase "if and only if" is symbolized with the "↔".

Accepted Answer

A) True 
 B)False

Question 14

In A → B,

Accepted Answer

A)  A provides a necessary condition for B. B. B provides a sufficient condition for A. 
C)  A provides a sufficient condition for B. 
D)  A provides both a necessary and sufficient condition for B.

Question 15

In A → B, the consequent is B.

Accepted Answer

A) True 
 B)False

Question 16

Where "F" stands for "Fred likes ice cream" and "L" stands for "Lou likes ice cream," the statement "Fred doesn't like ice cream only if Lou doesn't like ice cream" is best symbolized by

Accepted Answer

A)  ~F ⋁ ~L. B. ~F • ~L. 
C)  ~F → ~L. 
D)  ~(F • L).

Question 17

Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan will go to the Cayman Islands for spring break if and only if he gets an A on his geology mid-term, finishes his English research paper, and does not lose his job. (C: Nathan will go to the Cayman Islands for spring break; G: Nathan gets an A on his geology midterm; E: Nathan finishes his English research paper; J: Nathan loses his job.)

Accepted Answer

The answer of Translate the following statement into symbols, using...

Question 18

(A → B ⋁ C) is a well-formed formula.

Accepted Answer

A) True 
 B)False

Question 19

"All roses are red flowers" is a compound statement.

Accepted Answer

A) True 
 B)False

Question 20

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: ~(A → C) • (C ⋁ ~D)

Accepted Answer

A) True 
 B)False

Exam 7: Statement Logic: Truth Tables

A statement that is in at least one row is contingent.

Using a truth table, we can tell that an argument is valid if

A statement that is false regardless of the truth values assigned to the atomic statements that compose it is a contradiction.

"Chocolate is not nutritious" is an atomic statement.

In (A ⋁ B) → [B • (C ⋁ ~D) ], what is the main logical operator?

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: A ↔ (C ⋁ D)

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: B → ~(A • B)

Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true?

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: (A • B) → (A ⋁ ~(C ⋁ B))

The statement ~A ⋁ B is a negation.

The English phrase "if and only if" is symbolized with the "↔".

In A → B,

In A → B, the consequent is B.

Where "F" stands for "Fred likes ice cream" and "L" stands for "Lou likes ice cream," the statement "Fred doesn't like ice cream only if Lou doesn't like ice cream" is best symbolized by

(A → B ⋁ C) is a well-formed formula.

"All roses are red flowers" is a compound statement.

Making the assumption that A is , and D is false, determine the truth value () of this compound statement: ~(A → C) • (C ⋁ ~D)