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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) $\{-5, -4, -3, -2, -1\}$ $\newline$ (D) $\{-5, -3, -1\}$

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

\newline

(D)

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

Understand the problem: Understand the problem. We need to find the set of integers that are greater than or equal to $-5$ and less than or equal to $-1$ .
Identify inequality signs: Identify the inequality signs. The problem asks for numbers greater than or equal to $-5$ , which is represented by the inequality sign $\geq$ , and less than or equal to $-1$ , which is represented by the inequality sign $\leq$ .
Determine satisfying integers: Determine the set of integers that satisfy both conditions. The integers must be greater than or equal to $-5$ and at the same time less than or equal to $-1$ . This means we start at $-5$ and count up to $-1$ .
List integers: List the integers that satisfy both conditions. Starting from $-5$ and counting up to $-1$ gives us the set \{ $-5$ , $-4$ , $-3$ , $-2$ , $-1$ \}.
Match with choices: Match the set we found with the given choices. The correct set is $\{-5, -4, -3, -2, -1\}$ , which corresponds to choice (C).

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