Key Concepts: Conditional Statements

Conditional Statement

A conditional statement has the form "If p, then q" (written p → q). The hypothesis is p and the conclusion is q.

• A conditional is false ONLY when the hypothesis is true and the conclusion is false.

Related Conditionals

• Converse: If q, then p (q → p) — swap hypothesis and conclusion.
• Inverse: If not p, then not q (~p → ~q) — negate both.
• Contrapositive: If not q, then not p (~q → ~p) — swap AND negate.

Key Fact

A conditional and its contrapositive always have the same truth value. The converse and inverse also share the same truth value (but may differ from the original).

Biconditional

A biconditional statement (p ↔ q) means "p if and only if q." It is true when both p and q have the same truth value.