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

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Set-builder notation

Full solution

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

-3

and less than or equal to

2

?

\newline

Choices:

\newline

(A)

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

\newline

(B)

\{1, 2\}

\newline

(C)

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

\newline

(D)

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

Identify Inequality Signs: Identify the inequality signs and the type of numbers required. $\newline$ We need to find the set of integers that satisfy two conditions: they must be greater than or equal to $-3$ , and they must be less than or equal to $2$ . $\newline$ Inequality signs: $\geq$ (greater than or equal to) and $\leq$ (less than or equal to) $\newline$ Type of numbers: Integers
Find Integers Greater Than $-3$ : Determine the set of integers that are greater than or equal to $-3$ . Starting from $-3$ and moving upwards, the integers are $-3, -2, -1, 0, 1, 2, 3$ , and so on. However, we are only interested in the numbers up to $2$ .
Find Integers Less Than $2$ : Determine the set of integers that are less than or equal to $2$ . Starting from $2$ and moving downwards, the integers are $2, 1, 0, -1, -2, -3, -4$ , and so on. However, we are only interested in the numbers down to $-3$ .
Combine Results for Integer Set: Combine the results from Step $2$ and Step $3$ to find the set of integers that satisfy both conditions. $\newline$ The set of integers that are both greater than or equal to $-3$ and less than or equal to $2$ is $\{-3, -2, -1, 0, 1, 2\}$ .

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