2.1 Conditional Statements

Notes

A conditional is an if-then statement, $p \to q$. The "if" part $p$ is the hypothesis; the "then" part $q$ is the conclusion.

• Converse: $q \to p$ (switch). Inverse: not $p \to$ not $q$ (negate). Contrapositive: not $q \to$ not $p$ (switch and negate).
• A conditional and its contrapositive are always both true or both false.
• One counterexample proves a conditional false.
• Example: "If an angle measures $30^\circ$, then it is acute." Converse: "If an angle is acute, then it measures $30^\circ$." The converse is false; $50^\circ$ is a counterexample.