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Which is the set of integers greater than or equal to $-5$ and less than or equal to $-1$ ? $\newline$ Choices: $\newline$ (A) $\{-5, -2\}$ $\newline$ (B) $\{-5, -4, -3, -2\}$ $\newline$ (C) $\{-5, -3, -1\}$ $\newline$ (D) $\{-5, -4, -3, -2, -1\}$

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Set-builder notation

Full solution

Q. Which is the set of integers greater than or equal to

-5

and less than or equal to

-1

?

\newline

Choices:

\newline

(A)

\{-5, -2\}

\newline

(B)

\{-5, -4, -3, -2\}

\newline

(C)

\{-5, -3, -1\}

\newline

(D)

\{-5, -4, -3, -2, -1\}

Identify Inequality: Identify the inequality that represents the set of integers greater than or equal to $-5$ and less than or equal to $-1$ . The inequality for greater than or equal to is $\geq$ and for less than or equal to is $\leq$ . So, we are looking for the set of integers $x$ such that $-5 \leq x \leq -1$ .
List Integers: List all the integers that satisfy the inequality $-5 \leq x \leq -1$ . Starting from $-5$ and counting up to $-1$ , we get the integers $-5$ , $-4$ , $-3$ , $-2$ , and $-1$ . These are all the integers that are greater than or equal to $-5$ and less than or equal to $-1$ .
Match Choices: Match the list of integers with the given choices to find the correct set. $\newline$ (A) ${-5, -2}$ does not include all the integers between $-5$ and $-1$ . $\newline$ (B) ${-5, -4, -3, -2}$ is missing the integer $-1$ . $\newline$ (C) ${-5, -3, -1}$ is missing the integers $-4$ and $-2$ . $\newline$ (D) ${-5, -4, -3, -2, -1}$ includes all the integers from $-5$ to $-1$ . $\newline$ Therefore, the correct set is (D) ${-5, -4, -3, -2, -1}$ .

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