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