2. (2 points) Let S be the set of all students at a university, and let e Bo, Bi

Question

2. (2 points) Let S be the set of all students at a university, and let e Bo, Bi, B2, B3, B, Bs, where each set in the collection is described below. Does e give a partition of S? Justify your answer Bo is the set of students with no credit cards. B1 is the set of students with exactly one credit card. B2 is the set of students with exactly two credit cards. Ba is the set of students with exactly three credit cards Ba is the set of students with exactly four credit cards. Bs is the set of students with five or more credit cards.

Explanation / Answer

The previous collections are not necessarily partitions of the indicated sets. The set is mutually disjointed with no student belonging to more than one category, and the union of the collections is S. But unfortunately it does not pass the nonempty test because there may be sets that are empty. For example, there may be no students with exactly 4 credit cards. This would indicate that B, would be empty, and the collections would not be nonempty. Therefore, these collections are not partitions of the indicated sets

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