Use the Venn diagram to answer the following. List all the elements in the set $(A \cup B) \cap B'$. Answer {...} Fill in a set notation symbol to complete the statement below. Answer {3, 5, 8} ... A Use set notation to describe the shaded region.

1. Interpret the set expression and select the required region from the Venn diagram.

$A\cup B$ means all elements in $A$ or $B$:
$A\cup B=\{3,5,8,6,7,4\}.$
$B'$ means elements not in $B$. Therefore,
$(A\cup B)\cap B'=\text{elements in }A\cup B\text{ but not in }B=\{3,5,8\}.$

1. Recognise the relationship between $\{3,5,8\}$ and set $A$.

From the Venn diagram, $3,5,8$ are all elements inside set $A$. Hence $\{3,5,8\}$ is a proper subset of $A$.

So the missing symbol is $\subset$.

1. Describe the only unshaded region and take its complement to represent the shaded region.

The only unshaded region is the part in $A$ but not in $B$, which is $A \cap B'$.
Therefore the shaded region is its complement:
$(A \cap B')'$