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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 .
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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.
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 Variations of : • 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”,
