27,446 views
15 votes
15 votes
A set s consists of all real numbers between 17 and 21 , inclusive. Use set-builder notation to define s

A set s consists of all real numbers between 17 and 21 , inclusive. Use set-builder-example-1
User CarlosJavier
by
2.8k points

1 Answer

26 votes
26 votes

Answer: Choice C

============================================================

Step-by-step explanation:

The curly braces tell us we're dealing with a set of values.

The notation
x \in \mathbb{R} means "x is in the set of real numbers". In other words, it says "x is a real number".

Writing
17 \le x \le 21 tells the reader that x is between 17 and 21, including both endpoints.

Put everything together and
\{x|x\in\mathbb{R} \text{ and } 17 \le x \le 21\} means "we have a set of real numbers x that are between 17 and 21, inclusive".

-------------------------------

Extra info:

  • Choice A can be ruled out because there isn't any number that's both smaller than 17 and also larger than 21 at the same time. The set described for choice A simplifies to the empty set.
  • Choice B is ruled out because this is only talking about integers between 17 and 21; instead of real numbers. A number like 17.5 is left out when we want to include it.
  • Choice D can be ruled out because the endpoints x = 17 and x = 21 are left out (but we want to include them). Also, there's no mention if x is a real number or not.
User Ihab Shoully
by
2.4k points