Boyd/Usilton. Conditional If-then statement that contains a hypothesis (p) and a conclusion (q). Hypothesis(p): The part of the conditional following.

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Presentation transcript:

Boyd/Usilton

Conditional If-then statement that contains a hypothesis (p) and a conclusion (q). Hypothesis(p): The part of the conditional following if. Conclusion(q): The part of the conditional following then.

Identifying Hypothesis and Conclusion If and animal is a lion, then the animal is a mammal.

Writing a Conditional Complementary angles equal 90 degrees. 1. Identify hypothesis and conclusion. 2. Write the conditional. If two angles are complementary, then they equal 90 degrees.

Counterexamples Proves the conclusion is false. If a woman is born in Maine, then she is an American. Conclusion is true. If a woman is born in Maine, then she is catholic. Conclusion is false. Counterexample: Just because the woman was born in Maine does not mean that she is catholic.

Related Conditional Statements StatementHow to WriteExampleSymbols ConditionalUse given hypothesis and conclusion If m<A is 15, then <A is acute. p q ConverseFlip given hypothesis and conclusion. If <A is acute, then m<A is 15. q p InverseNegate given hypothesis and conclusion of the conditional. If m<A ≠15, then <A is not acute. -p -q ContrapositiveNegate given hypothesis and conclusion of the converse. If <A is not acute, then m<A ≠ 15. -q -p

Boyd/Usilton

Biconditionals A biconditional is a single true statement that combines a true conditional and its true converse. Write a biconditional by joining the two parts of each conditional with the phrase if and only if.

Writing Biconditionals If two angles have an equal measure, then the angles are congruent. Write the converse of the original conditional. If two angles are congruent, then they have an equal measure. If the converse if true, rewrite the statement as a biconditional. Two angles are congruent if and only if they have an equal measure.

Identifying the Conditionals in a Biconditional What are the two conditional statements that form the biconditional below? A ray is an angle bisector if and only if it divides an angle into two congruent angles. Identify the p (hypothesis) and q (conclusion) p: A ray is an angle bisector q: A ray divides an angle into two congruent angles. Write the conditional and the converse. Conditional: If a ray is an angle bisector, then it divides an angle in into two congruent angles. Converse: If a ray divides an angle into two congruent angles, then it is an angle bisector.