Discrete Mathematics and Its Applications, Seventh Edition

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

Chapter 12 - Section 12.1 - Boolean Functions - Exercises - Page 818: 2

Answer

a) x=0 b) x=0 c) There are two solutions, x = 0 and x = 1 d) There are no solutions

Work Step by Step

a) Since (x · 1 = x), the only solution is x = 0. b) Since (x + x = x) i.e. 0 + 0 = 0 and 1 + 1 = 1, the only solution is x = 0. c) Since this equation holds for all x, there are two solutions, x = 0 and x = 1. d) Since either x or (inverted)x must be 0, no matter what x is, there are no solutions.
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