Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.7 - Introduction to Proofs - Exercises - Page 91: 20

Answer

See the solution.

Work Step by Step

$Proof.$ The consequent of $P(1)$ is $1^2\geq 1$. We know $1^2=1$, so the consequent of $P(1)$ is $1\geq 1$, which is true. Thus since $P(1)$ is a conditional sentence with a true consequent, $P(1)$ is true.$_\Box$ We proved $P(1)$ is true by showing its consequent is true. Therefore, we used a trivial proof.
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