Conditional Statements Section 2.3 GEOMETRY
Conditional statements Form of conditional statement: If p then q (p implies q) Denote by p is called hypothesis, q is called conclusion Ex: If Bobcats win this game, then they will be number one.
Truth table for p q T F
Variations of a conditional statement Converse: Inverse: Contrapositive: is logically equivalent to its contrapositive Converse is logically equivalent to inverse
Examples of variations If Bobcats win this game, then they will be number one. Contrapositive: If Bobcats aren’t #1 then they didn’t win. Converse: If Bobcats are number one then they won the game. Inverse: If Bobcats don’t win this game then they will not be #1.
Other conditional statements “q only if p” means “if not p then not q” or, equivalently, “if q then p” “q if and only if p” means Other ways to say or to denote it: “biconditional of p and q”, “q iff p”,
Summary of conditional statements original statement converse statement biconditional statement if p then q q only if p q if and only if p p is sufficient condition for q p is necessary condition for q p is necessary and sufficient for q
Order of operations