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 819: 37

Answer

Showing that in a Boolean algebra, the complement of the element 0 is the element 1 and vice versa.

Work Step by Step

Because -- 0 ∨ 1 = 1 and 0 ∧ 1 = 0 by the identity and commutative laws, -- it follows that 0 = 1. Similarly, -- because 1 ∨ 0 = 1 and 1∧0 = 1, it follows that 1 = 0.
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