在韦恩图中，将代表 $Q \cup P^{\prime}$ 的区域涂上阴影。设 $\xi = \{\text{integers } x : 1 \le x \le 9\}$ 。韦恩图显示了 $\xi$ 的元素以及三个集合 $A$ 、 $B$ 和 $C$ 。使用下方符号之一完成每个陈述。符号：∅ ⊂ ⊄ ∈ ∉ ξ $\{4, 8\} \subset B$ $9 \in C$ $B \cap C = \varnothing$

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完整解法

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.

答案

Shade the inner circle $Q$ and the region outside the larger circle. Leave only the annular ring $P$ unshaded.

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