Conditional Statements

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Conditional Statements

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

Logical equivalences including
Example of the first equivalence: “Either Jim works hard or he gets F” is equivalent to “If Jim doesn’t work hard then he gets F”

Variations of a conditional statement
Contrapositive: Converse: Inverse: 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