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 12.2 - Representing Boolean Functions - Exercises - Page 822: 9

Answer

0

Work Step by Step

Showing that the Boolean sum y1 + y2 +· · ·+yn, - where yi = xi or yi = xi , has the value 0 for exactly one combination of the values of the variables, - namely, when xi = 0 if yi = xi and xi = 1 if yi = xi . -y1 + y2 + · · · + yn = 0 -if and only if yi = 0 for i = 1, 2, . . . , n. -This holds if and only if xi = 0 when yi = xi and xi = 1 when $~y_{i}$ = $~x_{i}$ .
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