2. 外语
  3. Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could

Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could

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问题 Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could be the number of members in set B that are not in set A ?
Indicate all such numbers.
A 3
B 5
C 13
D 25
E 50
F 53
选项
答案B，C，D，E
解析 Let x be the number of members in the intersection of set A and set B. Then the distribution of the members of A and B can be represented by the following Venn diagram.

The question asks you to indicate which of the answer choices could be the number of members in set B that are not in set A. This is equivalent to determining which of the answer choices are possible values of 53 - x.
You are given that the number of members in set A that are not in set B is at least 2, and clearly the number of members in set A that are not in set B is at most all 50 members of A; that is, 2 < 50 - x < 50. Note that 53 - x is 3 more than 50 - x. So by adding 3 to each part of 2 < 50 - x < 50, you get the equivalent inequality 5 < 53 - x < 53. Thus the number of members in set B that are not in set A can be any integer from 5 to 53. The correct answer consists of Choices B, C, D, E, and F.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 2: Translate from Words to a Figure or Diagram
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