Discrete Mathematics and Its Applications, Seventh Edition

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

Chapter 2 - Section 2.1 - Sets - Exercises - Page 126: 43

Answer

Done below.

Work Step by Step

a) If $x^2 < 3$, then $-\sqrt{3} < x < \sqrt{3}$. Since $\sqrt{3}$ is about 1.7, the statement is true if and only if $x$ is in the set $\{-1, 0, 1\}$ b) If $x^2 > x$, then $x^2 - x > 0$ so that $x(x - 1) > 0$. This obviously fails for $x = 0, 1$, but any other integer will yield a positive value. c) If $2x + 1 = 0$, then $x = -1/2$. Thus the truth set is just the empty set.
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