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Let A and B be subsets of the finite universal set U. Show

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 12E Chapter 2.SE

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 12E

Let A and B be subsets of the finite universal set U. Show that

Step-by-Step Solution:

SolutionStep 1Let us assume that A and B are the subsets of the finite universal set U.Use the De Morgan’s Law|| = || || = ||Use the properties of Universal SetU = || + |A B| || = |U| - |A B|Now, Use the Principle of Exclusion and Inclusion|A B| = |A| + |B| - |AB| || = |U| - (|A| + |B| - |AB|) = |U| - |A| - |B| + |AB|Hence, it is proved that || = |U| - |A| - |B| + |AB|

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Chapter 2.SE, Problem 12E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Let A and B be subsets of the finite universal set U. Show