On the Venn diagram, shade the region which represents $Q \cup P^{\prime}$. Let $\xi = \{\text{integers } x : 1 \le x \le 9\}$. The Venn diagram shows the elements of $\xi$ and three sets $A$, $B$ and $C$. Use one of the symbols below to complete each statement. Symbols: ∅ ⊂ ⊄ ∈ ∉ ξ $\{4, 8\} \subset B$ $9 \in C$ $B \cap C = \varnothing$

1. Identify the complement of $P$ on the diagram

$P'$ means all regions not in $P$.

Since $P$ is the annular ring, $P'$ consists of the inner disc $Q$ and the region outside the larger circle.

2. Apply the union with $Q$ and state the shaded region

$Q \cup P'$ means shade all elements in $Q$ or in $P'$.

But $Q$ is already included in $P'$, so
$Q \cup P' = P'.$

Therefore shade $Q$ and everything outside the larger circle, leaving the ring $P$ unshaded.