## Thinking Mathematically (6th Edition)

$\{a, c, d, e, f, g, h\}$
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 $(A\cap B)\cup B'$ The intersection of sets $A$ and $B$ ($A\cap B$) is a set containing every element of $A$ that is also an element of $B$. $A\cap B=\{g, h\}$ The complement of $B$ ($B'$) is a set that contains every elements of $U$ that isn't contained in $B$. $B'=\{a, c, d, e, f\}$ Finally, $\cup$ indicates that the resulting set should have all distinct elements that are present in either of the 2 sets. $(A\cap B)\cup B'=\{g, h\}\cup\{a, c, d, e, f\}=\{a, c, d, e, f, g, h\}$