Philosophy 1102 Module 7 Quiz

Which of the following is not a well-formed formula (WFF)?

(~A → B ⋁ C)

Which of the following is an atomic statement?

sailing is an enjoyable sport

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

there is no row where the premises are true and the conclusion is false.

Where "F" stands for "Fred likes ice cream" and "L" stands for "Lou likes ice cream," the statement "Neither Fred nor Lou likes ice cream" is best symbolized by

~F • ~L.

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

~F → ~L.

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

~F ⋁ ~L.

The consequent of a true conditional statement provides a necessary condition for the truth of the antecedent.

True

Two statements are logically equivalent when the biconditional connecting them is a tautology.

True

A material conditional is false if its antecedent is true and its consequent is false; otherwise, it is true.

True

An argument is valid when it is not possible for its conclusion to be false when all of its premises are true.

True

Any argument with logically inconsistent premises will be valid yet unsound.

True

If there is any assignment of truth values in which the premises are all true and the conclusion is false, then the argument is invalid.

True

In A → B, the consequent is B.

True

In A ⋁ (B • C), the main logical operator is the "⋁".

True

Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true? (Use a truth table to determine the answer. You do not need to submit the truth table.)

A is false, B is false, and C is false.

Under which assignment of truth values does the sentence (A ↔ ~B) • ~C turn out to be true? (Use a truth table to determine the answer. You do not need to submit the truth table.)

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

On which assignment of truth values does the sentence A → ~B turn out to be false? (Use a truth table to determine the answer. You do not need to submit the truth table.)

A is true, and B is true.

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

True

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

True

"Chocolate is not nutritious" is an atomic statement.

False

(A → (B ⋁ C) ⋁ D) is a well-formed formula.

False

(A → B ⋁ C) is a well-formed formula.

False

A conjunction is true if either one of its conjuncts is true; otherwise, it is false.

False

In A • B, the statement constants are called disjuncts.

False

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

False

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

False

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

True

A compound statement is a tautology if

it is true regardless of the truth values assigned to its component atomic sentences.

A compound statement is truth-functional if

its truth value is a function of the truth value of its component atomic statements.