## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 2 - Set Theory - 2.3 Venn Diagrams and Set Operations - Exercise Set 2.3 - Page 81: 56

#### Answer

$(A\cup C)'=\{\}$

#### Work Step by Step

We are given: $U = \{a, b, c, d, e, f, g, h\}$ $A = \{a, g, h\}$ $B = \{b, g, h\}$ $C = \{b, c, d, e, f\}$ We need to determine $(A\cup C)'$ The union of sets $A$ and $C$ ($A\cup C$) is a set that has all the distinct elements of both $A$ and $C$. $A\cup C=\{a, b, c, d, e, f, g, h\}$ The ($'$) outside of the bracket indicates that we need a complement of $(A\cup C)$: the resulting set should contain the elements in the universal set $U$ that are not in $(A\cup C)$. $(A\cup C)'=\{\}$

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