Question

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

Answer 1

Answer: Choice C

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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".

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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.