Logical Equivalence Quiz

What is the symbol used in referring to logically equivalent propositions?

• ∧

• ∨

• ⟺

• ↔

Which of the following supports the logical equivalence ~[푝∨(~푝∧푞)]⟺(~푝)∧~(~푝∧푞)?

• De Morgan’s Law

• Identity Law

• Idempotent Law

• Double Negation

Which of the following supports the logical equivalence (~푝)∧~(~푝∧푞)⟺~푝∧[~(~푝)∨(~푞)?

• Double Negation

• Identity Law

• Idempotent Law

• De Morgan’s Law

Which of the following supports the logical equivalence ~푝∧[~(~푝)∨(~푞)⟺~푝∧(푝∨~푞)?

• Double Negation

• Identity Law

• Idempotent Law

• De Morgan’s Law

Which of the following supports the logical equivalence ~푝∧(푝∨~푞)⟺(~푝∧푝)∨(~푝∧~푞)?

• Associative Law

• Commutative Law

• Distributive Law

• Switcheroo Law

Which of the following supports the logical equivalence (~푝∧푝)∨(~푝∧~푞)⟺휙∨(~푝∧~∧푞)?

• Switcheroo Law

• Domination Law

• Absorption Law

• Inverse Law

Which of the following supports the logical equivalence 휙∨(~푝∧~∧푞)⟺~푝∧~푞?

• Domination Law

• Idempotent Law

• Identity Law

• Double Negation

Which of the following logical equivalence is being depicted by 푝∧(푞∧푟)⟺(푝∧푞)∧푟?

• Identity Law

• Commutative Law

• Associative Law

• Distributive Law

Which of the following are logically equivalents?

• converse and contrapositive

• contrapositive and conditional

• conditional and inverse

• conditional and converse

What type of conditionals is being depicted by the conditional statement, “If a quadrilateral is not a square, then it does not have equal sides.”?

• converse

• contrapositive

• inverse

• equivalence