Biconditional: Points lie on the same line if and only if they are collinear.
For a biconditional statement to be true, both the conditional statement and its converse must be true. If either the conditional or the converse is false, then the biconditional statement is false.
Determine if the biconditional is true. If false, give a counterexample. Example 3A: Analyzing the Truth Value of a Biconditional Statement A rectangle has side lengths of 12 cm and 25 cm if and only if its area is 300 cm 2 .
Check It Out! Example 3a An angle is a right angle iff its measure is 90°. Determine if the biconditional is true. If false, give a counterexample.
Lesson Quiz: Part I Identify the hypothesis and conclusion of each conditional. 1. A triangle with one right angle is a right triangle. 2. All even numbers are divisible by 2. 3. Determine if the statement “If n 2 = 144, then n = 12” is true. If false, give a counterexample.
Lesson Quiz: Part II Identify the hypothesis and conclusion of each conditional. 4. Write the converse, inverse, and contrapositive of the conditional statement “If Maria’s birthday is February 29, then she was born in a leap year.” Find the truth value of each.
p q p → q T T T T F F F T T F F T So p → q follows the following reasoning: • a True premise implies a True conclusion, therefore T → T is T; • a True premise cannot imply a False conclusion, therefore T → F is F; and • you can conclude anything from a false assumption, so F → anything is T.
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- Summer '18
- Jane Smith