4 Logical equivalences including Example of the first equivalence:“Either Jim works hardor he gets F”is equivalent to“If Jim doesn’t work hardthen he gets F”
5 Variations of a conditional statement Contrapositive:Converse:Inverse:is logically equivalent to its contrapositiveConverse is logically equivalent to inverse
6 Examples of variations If Bobcats win this game,then they will be number one.Contrapositive: If Bobcats aren’t #1then they didn’t win.Converse: If Bobcats are number onethen they won the game.Inverse: If Bobcats don’t win this gamethen they will not be #1.
7 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” meansOther ways to say or to denote it:“biconditional of p and q”,“q iff p”,
8 Summary of conditional statements original statementconverse statementbiconditional statementif p then qq only if pq if and only if pp is sufficient condition for qp is necessary condition for qp is necessary and sufficient for q