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Which is the set of integers greater than $-6$ and less than or equal to $-2$ ? $\newline$ Choices: $\newline$ (A) $\{-6, -4, -2\}$ $\newline$ (B) $\{-5, -4, -3, -2\}$ $\newline$ (C) $\{-6, -5, -4, -3, -2\}$ $\newline$ (D) $\{-5, -4, -3\}$

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Set-builder notation

Full solution

Q. Which is the set of integers greater than

-6

and less than or equal to

-2

?

\newline

Choices:

\newline

(A)

\{-6, -4, -2\}

\newline

(B)

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

\newline

(C)

\{-6, -5, -4, -3, -2\}

\newline

(D)

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

Identify Inequality: Identify the inequality that represents the condition ＂greater than $-6$ and less than or equal to $-2$ ＂. $\newline$ Inequality: $-6 < x \leq -2$
Determine Integers: Determine the set of integers that satisfy the inequality $-6 < x \leq -2$ . The integers greater than $-6$ are $-5, -4, -3, -2, -1, 0, 1, 2, \ldots$ However, we need to stop at $-2$ because the inequality states that $x$ must be less than or equal to $-2$ .
Exclude $-6$ from Set: Exclude $-6$ from the set because the inequality specifies that $x$ must be greater than $-6$ , not equal to it. $\newline$ The set of integers that satisfy the inequality is $\{-5, -4, -3, -2\}$ .

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