2. 外语
  3. CIn this question, you are given that set S consists of 5 objects and are asked to compare the number of subsets of set S that c

CIn this question, you are given that set S consists of 5 objects and are asked to compare the number of subsets of set S that c

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答案C
解析 In this question, you are given that set S consists of 5 objects and are asked to compare the number of subsets of set S that consist of 1 object with the number of subsets of set S that consist of 4 objects. Recall that a set R is a subset of set S if all of the members of R are also members of S.
    Note that if you select 1 object from set S, there are 4 objects in S that you have not selected; that is to say, each subset of S with 1 object corresponds to a subset of S with 4 objects. Therefore, the number of subsets of S with 1 object is equal to the number of subsets of S with 4 objects. Since Quantity A is equal to Quantity B, the correct answer is Choice C.
    Another approach to solving this problem is to consider a particular set of 5 objects and determine all of the subsets consisting of 1 object and all of the subsets consisting of 4 objects. For example, let S = {a, b, c, d, e}. There are 5 subsets of S consisting of 1 object: {a}, {b}, {c}, {d}, and {e}; there are 5 subsets of S consisting of 4 objects: {a, b, c, d}, {a, b, c, e}, {a, b, d, e}, {a, c, d, e}, and {b, c, d, e}.
Clearly, the particular 5 objects in S do not change the fact that the number of subsets of S consisting of 1 object is equal to the number of subsets of S consisting of 4 objects. The correct answer is Choice C.
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