Biconditionals and Good Definitions
Learn how to write biconditionals, understand the importance of good definitions that can be expressed as biconditionals, and identify the converse of true conditionals. Explore examples and enhance your knowledge of logical statements.
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Presentation Transcript
2-3 Biconditionals and Definitions Objective: To write biconditionals and recognize good definitions
A biconditional is a single true statement that combines a true conditional and its true converse.
Remember: A conditional is an if-then statement including a hypothesis and a conclusion. A converse is obtained by reversing the hypothesis and conclusion of the conditional You can write a biconditional by joining the two parts of each conditional with the phrase if and only if.
Essential Understanding: A definition is good if it can be written as a biconditional. What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional. If two angles have equal measure, then the angles are congruent. Converse: If two angles are congruent, then the angles have equal measure; TRUE Biconditional: Two angles have equal measure if and only if the angles are congruent.
What are the two conditionals that form this biconditional? Two numbers are reciprocals if and only if their product is 1. If two numbers are reciprocals, then their product is 1. If the product of two numbers is 1, then the numbers are reciprocals.
