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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) $\{1, 2\}$ $\newline$ (B) $\{-3, -2, -1\}$ $\newline$ (C) $\{-3, -2, -1, 0, 1, 2\}$ $\newline$ (D) $\{-2, -1, 0, 1, 2\}$

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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)

\{1, 2\}

\newline

(B)

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

\newline

(C)

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

\newline

(D)

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

Identify Inequality Signs and Range: Identify the inequality signs and the range of integers needed. $\newline$ We are looking for integers that are greater than or equal to $-3$ and less than or equal to $2$ . The inequality signs we are dealing with are ＂greater than or equal to＂ ( $\geq$ ) and ＂less than or equal to＂ ( $\leq$ ).
List Integers $\geq -3$ : List the integers that satisfy the first part of the inequality, which is greater than or equal to $-3$ . The integers greater than or equal to $-3$ are: $-3, -2, -1, 0, 1, 2, 3, 4, \ldots$
List Integers $\leq 2$ : List the integers that satisfy the second part of the inequality, which is less than or equal to $2$ . $\newline$ The integers less than or equal to $2$ are: $..., -3, -2, -1, 0, 1, 2$ .
Find Intersection of Sets: Find the intersection of the two sets from Step $2$ and Step $3$ to get the integers that satisfy both conditions. $\newline$ The intersection of the two sets is: ${-3, -2, -1, 0, 1, 2}$ .
Match with Choices: Match the resulting set with the given choices to find the correct answer. $\newline$ The correct set is $(C)\{-3, -2, -1, 0, 1, 2\}$ .

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