Question

集合 $A$ 有 $20$ 个元素，集合 $B$ 有 $15$ 个元素。 $A \cup B$ ，即 $A$ 和 $B$ 的并集，最少可能有多少个元素？

Set $A$ has $20$ elements, and set $B$ has $15$ elements. What is the smallest possible number of elements in $A \cup B,$ the union of $A$ and $B?$

$5$

$15$

$20$

$35$

$300$

要使并集元素数最少，就要让两个集合重叠尽可能多。

可以让 $B$ 完全包含于 $A$ ，此时并集就是 $A$ ，共有 $20$ 个元素。

所以正确答案是 C。

To minimize the number of elements in the union, we want to maximize the overlap between the two sets.

We can then assume that $B$ is contained completely within $A,$ which means that the union is the same as $A,$ which has $20$ elements.

Thus, C is the correct answer.