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Logical Arguments and Validity Quiz

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Questions and Answers

Which of the following is the correct definition of a tautology?

A statement formula that is logically equivalent to its negation.
A statement formula whose truth value is always True for any assignment of truth values to its variables. (correct)
A statement formula whose truth value is always False for any assignment of truth values to its variables.
A statement formula that is logically equivalent to the conjunction of two contradictory statements.

If A and B are statement formulas and A ⟷ B is a tautology, what can we conclude?

A is a contradiction and B is a tautology.
A and B are both contradictions.
A and B are logically equivalent. (correct)
A is a tautology and B is a contradiction.

Which of the following is an example of a contradiction?

$(p \lor \sim p)$
$(p \land \sim p)$ (correct)
$(p \land q)$
$(p \lor q)$

Which of the following logical equivalences represents the commutative law for disjunction?

$(p \lor q) \equiv (q \lor p)$ (D) Signup and view all the answers

Which of the following represents the absorption law for conjunction?

$(p \lor (p \land q)) \equiv p$ (B) Signup and view all the answers

If ⊨ (A → B) and ⊨ A, what can we conclude about B?

⊨ B (D) Signup and view all the answers

Which of the following represents the double negation law?

$(\sim (\sim p)) \equiv p$ (D) Signup and view all the answers

Which of the following represents the distributive law for disjunction over conjunction?

$(p \land (q \lor r)) \equiv ((p \land q) \lor (p \land r))$ (C) Signup and view all the answers

If A and B are statement formulas and A ⟷ B is a contradiction, what can we conclude?

A and B are not logically equivalent. (B) Signup and view all the answers

Which of the following represents the idempotent law for conjunction?

$(p \land p) \equiv p$ (B) Signup and view all the answers