10 Questions
Which of the following is the correct definition of a tautology?
A statement formula whose truth value is always True for any assignment of truth values to its variables.
If A and B are statement formulas and A ⟷ B is a tautology, what can we conclude?
A and B are logically equivalent.
Which of the following is an example of a contradiction?
$(p \land \sim p)$
Which of the following logical equivalences represents the commutative law for disjunction?
$(p \lor q) \equiv (q \lor p)$
Which of the following represents the absorption law for conjunction?
$(p \lor (p \land q)) \equiv p$
If ⊨ (A → B) and ⊨ A, what can we conclude about B?
⊨ B
Which of the following represents the double negation law?
$(\sim (\sim p)) \equiv p$
Which of the following represents the distributive law for disjunction over conjunction?
$(p \land (q \lor r)) \equiv ((p \land q) \lor (p \land r))$
If A and B are statement formulas and A ⟷ B is a contradiction, what can we conclude?
A and B are not logically equivalent.
Which of the following represents the idempotent law for conjunction?
$(p \land p) \equiv p$
Test your understanding of logical arguments and validity with this quiz. Topics covered include Modus Ponens, Modus Tollens, Disjunctive Syllogism, Hypothetical Syllogism, Dilemma, Conjunctive Simplifications, Disjunctive Additions, and Conjunction Additions.
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