Using correct mathematical notation and symbols, express the following in set-builder notation:

Z = {16, 17, 18, 19, 20}

I'm so confused with this....please help :(

do it the same way I just showed you in the other post.

the numbers are between 15 and 20, and they are natural numbers.

{x | 15 < x < 20, x ∈ N} ??

or would it be this {x | 15 < x < 20, x ∈ z} ???

That would work, except say 15<x<21, that was my error.

I would use x ∈ N , since the numbers 15 and 20 were not part of the set Z

or you could say

{x | 16 ≤ x ≤ 20, x ∈ z}

btw, I should have had the original above as
{x | 15 < x < 21, x ∈ N}

The way I had it, the 20 would have been excluded.

So your saying this question:

Express the following in roster form: Set M is the set of natural numbers between fourteen and nineteen, would be
{x | 15 < x < 21, x ∈ N} ??

Please read my replies above including the correction

you want the numbers 16,17,18,19,20

they can be expressed
either as
16≤x≤20 , x∈N
or
15<x<21, x∈N

Sure! In order to express the set Z = {16, 17, 18, 19, 20} in set-builder notation, we need to specify the condition or rule that describes the elements in the set.

In this case, the rule can be stated as follows:

Z = {x | x is an element of the set of integers, and 16 ≤ x ≤ 20}

Let me break it down for you:

- The symbol | (read as "such that") separates the variable x from the condition.
- The variable x represents any element that satisfies the condition.
- The condition itself consists of two parts:
- x is an element of the set of integers: This indicates that x must be an integer. This is denoted by the symbol Z, which represents the set of integers.
- 16 ≤ x ≤ 20: This specifies that x must be greater than or equal to 16 and less than or equal to 20. The ≤ symbol represents "less than or equal to."

Combining all the elements, the set Z = {16, 17, 18, 19, 20} can be expressed in set-builder notation as:

Z = {x | x ∈ Z, 16 ≤ x ≤ 20}

I hope this clears up your confusion! Let me know if you have any other questions.