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Which is the set of integers greater than $-3$ and less than or equal to $0$ ? $\newline$ Choices: $\newline$ (A) $\{-2, -1\}$ $\newline$ (B) $\{-3, 0\}$ $\newline$ (C) $\{-3, -2, -1, 0\}$ $\newline$ (D) $\{-2, -1, 0\}$

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Set-builder notation

Full solution

Q. Which is the set of integers greater than

-3

and less than or equal to

0

?

\newline

Choices:

\newline

(A)

\{-2, -1\}

\newline

(B)

\{-3, 0\}

\newline

(C)

\{-3, -2, -1, 0\}

\newline

(D)

\{-2, -1, 0\}

Identify Range: Let's first identify the range of integers we are looking for. We need to find the set of integers that are greater than $-3$ and less than or equal to $0$ .
Inequality for $-3$ : The inequality that represents numbers greater than $-3$ is $x > -3$ . However, since we are looking for integers, we need to consider the smallest integer that is greater than $-3$ , which is $-2$ .
Inequality for $0$ : The inequality that represents numbers less than or equal to $0$ is ＂ $x \leq 0$ ＂. This means that the largest integer we are considering is $0$ .
Combine Inequalities: Combining both inequalities, we are looking for integers $x$ such that $-2 \leq x \leq 0$ . This includes the integers $-2$ , $-1$ , and $0$ .
Match Criteria: Looking at the choices given, the set that matches our criteria is (D) ${-2, -1, 0}$ .

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