Question

Select all of the following that would be an acceptable set builder notation for the set {7, 8, 9, 10, 11, 12, 13, 14}.

Answer 1

Answer: Choice B

{x | x is a natural number with 6 < x < 15}

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Explanation:

The given set is in roster notation. Think of a baseball or football team (or any sports team) how their roster lists out all of the players. In this case, each number is like a player.

The idea here is to simplify the set so we don't have to write out every single item. Instead we have a rule to make things a bit simpler.

In this case, the set {7, 8, 9, 10, 11, 12, 13, 14} describes all natural numbers from 7 to 14

This means we can say {x | x is a natural number with 6 < x < 15}

Note how the endpoints x = 6 and x = 15 are not included. This is because there isn't a "or equal to" as part of the inequality sign. Sure enough 6 and 15 are not part of the original set.

An equivalent set would be $\{ x | \text{ x is a natural number with } \ 7 \le x \le 14\}$ and here we have "or equal to" involved. For this example, the endpoints x = 7 and x = 14 are included.

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Something like choice A and choice D are not complete answers because we don't know if x is a whole number, natural number, rational number, real number, etc. If x was say a real number, then x = 10.75 would be involved with choice A. But 10.75 is not part of the original set.