2011 AMC 10A 第 6 题

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

答案：C

知识点：韦恩图极限情形界定

难度评级：660

小提示：

并集必须包含较大集合的所有元素。

The union must contain all elements of the larger set

大提示：

让

B

成为

A

的子集可使并集最小。

Make

B

a subset of

A

to minimize the union

解答：

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.

2011 AMC 10A 第 6 题

答案：C

难度评级：660

小提示：

大提示：

解答：

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