The statement formed by negating the hypothesis and conclusion of a conditional statement Inverse Symbolic Notation: The equivalent statement formed by exchanging AND negating the hypothesis and conclusion of a conditional statement Contrapositive Symbolic Notation: Two statements that are both true or both false Equivalent Statements Conditional and Contrapositive; Converse and Inverse Ex. A statement that contains the and phrase “if only if.” Biconditional Combines a conditional and its converse when both are true. Statement Definitions are biconditionals Ex. Two lines that intersect to form right Perpendicular angles Lines Notation: Show: Rewrite the conditional statement in if-then form. Ex 1: All whales are mammals. If an animal is a whale, then it is a mammal. Three points are collinear when there is a line containing them. If there is a line containing three points, then the points are collinear. Write the if-then form, the converse, the inverse, and the contrapositive of the Ex 2: statement, then determine the validity of each statement. Statement: Soccer players are athletes Conditional: If you are a soccer player, then you are an athlete. True. Converse: If you are an athlete, then you are a soccer player. False. Inverse: If you are not a soccer player, then you are not an athlete. False. Contrapositive: If you are not an athlete, then you are not a soccer player. True.
Inverse The statement formed by negating the hypothesis and conclusion of a conditional statement Symbolic Notation: Contrapositive The equivalent statement formed by exchanging AND negating the hypothesis and conclusion of a conditional statement Symbolic Notation: Equivalent Statements Two statements that are both true or both false Ex. Conditional and Contrapositive; Converse and Inverse Biconditional Statement A statement that contains the phrase “if and only if.” Combines a conditional and its converse when both are true. Ex. Definitions are biconditionals Perpendicular Lines Two lines that intersect to form right angles Notation: Show: Ex 1: Rewrite the conditional statement in if-then form. All whales are mammals. If an animal is a whale, then it is a mammal. Three points are collinear when there is a line containing them. If there is a line containing three points, then the points are collinear. Ex 2: Write the if-then form, the converse, the inverse, and the contrapositive of the statement, then determine the validity of each statement. Statement: Soccer players are athletes Conditional: If you are a soccer player, then you are an athlete. True. Converse: If you are an athlete, then you are a soccer player. False. Inverse: If you are not a soccer player, then you are not an athlete. False. Contrapositive: If you are not an athlete, then you are not a soccer player. True.
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