## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 2 - Set Theory - 2.4 Set Operations and Venn Diagrams with Three Sets - Exercise Set 2.4 - Page 92: 58

#### Answer

Sets (AUB')' and A'∩B are equal. As the regions of both the sets are same.

#### Work Step by Step

Set A' represents all the regions belongs to universal set U that does not belongs to A So, The regions III & IV represents the set A'. Set B' represents all the regions belongs to universal set U that does not belongs to B So, The regions I and IV represents the set B'. a) Set AUB' represents all the regions of set A and set B'. And (AUB')' represents the all the regions belongs to universal set U that does not belongs to (AUB'). So, The regions III represents the set (AUB')'. a) Set A'∩B represents the common regions of set A' and B So, The region III represents the set (A'∩B). Based on parts a and b, sets (AUB')' and A'∩B are equal. As the regions of both the sets are same.

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