Logical Equivalences Involving Conditional Statements

Vocabulary flashcards summarizing the key logical equivalences for conditional statements presented in the lecture notes.

Contrapositive Equivalence

p → q is logically equivalent to ¬q → ¬p.

Conditional–Disjunction Equivalence

p → q is logically equivalent to ¬p ∨ q.

Conjunction via Negated Conditional

p ∧ q is logically equivalent to ¬(p → ¬q).

Negation of a Conditional

¬(p → q) is logically equivalent to p ∧ ¬q.

Common Antecedent Conjunction

(p → q) ∧ (p → r) is logically equivalent to p → (q ∧ r).

Common Consequent Conjunction

(p → r) ∧ (q → r) is logically equivalent to (p ∨ q) → r.

Common Antecedent Disjunction

(p → q) ∨ (p → r) is logically equivalent to p → (q ∨ r).

Common Consequent Disjunction

(p → r) ∨ (q → r) is logically equivalent to (p ∧ q) → r.