## Thinking Mathematically (6th Edition)

$\{a\}$
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. $(A\cup B)\cap B'=\{a, b, g, h\}\cap\{a, c, d, e, f\}=\{a\}$