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

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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)

\{-3, 0\}

\newline

(C)

\{-2, -1, 0\}

\newline

(D)

\{-2, -1\}

Identify Inequality: Identify the inequality that represents the condition ＂greater than $-3$ and less than or equal to $0$ ＂. $\newline$ Inequality: $-3 < x \leq 0$
Determine Integers: Determine the set of integers that satisfy the inequality $-3 < x \leq 0$ . The integers greater than $-3$ are $-2$ , $-1$ , $0$ , $1$ , $2$ , ... However, we also need to consider that $x$ must be less than or equal to $0$ . Therefore, we exclude any integers greater than $0$ .
List Satisfying Integers: List the integers that satisfy both conditions: greater than $-3$ and less than or equal to $0$ . $\newline$ The integers that satisfy both conditions are $-2$ , $-1$ , and $0$ .
Match with Choices: Match the set of integers from Step $3$ with the given choices. $\newline$ The correct set of integers is $\{-2, -1, 0\}$ , which corresponds to choice (C).

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