Which of the following are sets? If the collection is not a set, explain why. If

Question

Which of the following are sets? If the collection is not a set, explain why. If it is a set, describe two larger sets whose intersection is the described set. For instance, "the collection of all multiples of 6" is equal to the intersection of the set of multiples of 2 and the set of multiples of 3. There are multiple possible choices for the larger set, but neither of them can be equal to the given set (so your answer cannot simply be the intersection of the set integers and the set of multiples of 6). (a) The collection of all even integers. (b) The collection of the ten best math books ever written. (c) The collection of Mercyhurst faculty members that live in Erie. (d) The collection of old buildings on the Mercyhurst Erie campus. (e) The collection of polynomials p(x) such that p(9) = 2.

Explanation / Answer

a. Is a set, it's an intersection of two larger sets which are set of all even numbers and the set of integers.

b. Can't be a set because best math books is an ambiguous term,the term best can differ from person to person hence the set is not defined.

c.yes,it can be set because the address of the faculty members can be arranged in a list area wise and any faculty member will live in one place at a time.

c. The term old is ambiguous, the parameter to define old is not mentioned. It could be a set if the year of construction of the buildings are taken into account. Since,some building might not appear old even if they are won't be in the set.

e. Yes, it's a set.

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