Geometry: Common Core (15th Edition)

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

Chapter 2 - Reasoning and Proof - 2-2 Conditional Statements - Practice and Problem-Solving Exercises - Page 94: 28



Work Step by Step

The conditional and contrapositive always have the same truth value. Since $2^2=4$, the conditional statement is true. The contrapositive both swaps and negates the hypothesis and the conclusion. If $x^2\ne4$, then $x\ne2$. Since $2^2=4$, the contrapositive is true. There is no counterexample. It is not necessary to find a counterexample to prove a statement is true. A counterexample can only prove a statement is false.
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