Answer
$\{a\}$
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 $(A\cup B)\cap B'$
The union of sets $A$ and $B$ ($A\cup B$) is a set containing all distinct elements that are present in either $A$ or $B$.
$A\cup B=\{a, b, g, h\}$
The complement of $B$ ($B'$) is a set that contains every element of $U$ that isn't contained in $B$.
$B'=\{a, c, d, e, f\}$
Finally, $\cap$ indicates that the resulting set should have all distinct elements of one set that are also present in the other.
$(A\cup B)\cap B'=\{a, b, g, h\}\cap\{a, c, d, e, f\}=\{a\}$
