2. 外语
  3. CIn this question, you are given that the number of integers in set A is 40, the number of integers in set B is 150, and the num

CIn this question, you are given that the number of integers in set A is 40, the number of integers in set B is 150, and the num

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问题
选项
答案C
解析 In this question, you are given that the number of integers in set A is 40, the number of integers in set B is 150, and the number of integers that are in both A and B is 20. You are asked to compare the total number of integers that are in set A or set B, or both, with 170.
    This is the type of question for which a Venn diagram is usually helpful to represent the information given. The following Venn diagram is a representation of the integers in sets A and B.

    Note that there is no number in the shaded region of the diagram—the region representing the integers in both A and B. In fact, the number of integers in both A and B is included in both the number of integers in A and the number of integers in B. It is a good idea, therefore, to redraw the Venn diagram so that the numbers are separated into three categories: the integers in A only, the integers in B only, and the integers in both A and B. The revised Venn diagram follows.

Observe that summing the numbers of integers in set A only, set B only, and both A and B yields the total number of integers that are in set A or set B, or both. Therefore, Quantity A is 20 + 130 + 20, or 170, and the correct answer is Choice C.
    Another approach is to realize that if you listed the integers in set A and the integers in set B, you would have listed the integers that are in both A and B twice and all of the other integers once. So the total number of integers in set A or set B, or both, is equal to
             (number in set A)+(number in set B)-(number in both sets)
Thus, the number of integers in set A or set B, or both, is 40 + 150 - 20, or 170, and the correct answer is Choice C.
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