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

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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)

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

\newline

(B)

\{-2, -1\}

\newline

(C)

\{-2, -1, 0\}

\newline

(D)

\{-3, 0\}

Identify Range of Integers: Let's first identify the range of integers we are looking for. We need a set of integers that are greater than $-3$ and at the same time less than or equal to $0$ .
Consider Greater Than $-3$ : Now, let's consider the inequality greater than $-3$ . This means we are looking for integers that are $-2$ , $-1$ , $0$ , and so on, but not $-3$ itself because the inequality is strict (not including $-3$ ).
Consider Less Than or Equal to $0$ : Next, let's consider the inequality less than or equal to $0$ . This means we are looking for integers that are $0$ , $-1$ , $-2$ , and so on, up to and including $0$ .
Combine Both Inequalities: Combining both inequalities, we need to find integers that satisfy both conditions: greater than $-3$ and less than or equal to $0$ . This means we are looking for the set of integers that start from $-2$ (the first integer greater than $-3$ ) and go up to $0$ (the last integer that is less than or equal to $0$ ).
Set of Integers: The set of integers that satisfy both conditions is $\{-2, -1, 0\}$ . This set includes all integers that are greater than $-3$ and less than or equal to $0$ .

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