Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-3 Biconditionals and Definitions - Practice and Problem-Solving Exercises - Page 101: 12


Converse: If $\sim q\ \longrightarrow\ \sim p$ is true, then $p\ \longrightarrow\ q$ is true. Biconditional: $p\ \longrightarrow\ q$ is true if and only if $\sim q\ \longrightarrow\ \sim p$ is true. A conditional and its contrapositive have the same truth value.

Work Step by Step

To write the converse of a conditional statement, write a new conditional statement that switches the hypothesis and conclusion. To write a biconditional, join the hypothesis and the conclusion with the term "if and only if".
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