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

\{-2, -1, 0\}

\newline

(B)

\{-2, -1\}

\newline

(C)

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

\newline

(D)

\{-3, 0\}

Identify Inequality: Identify the inequality that represents the condition ＂greater than $-3$ and less than or equal to $0$ ＂. $\newline$ The inequality for ＂greater than $-3$ ＂ is $x > -3$ , and for ＂less than or equal to $0$ ＂ is $x \leq 0$ .
Determine Integers: Determine the set of integers that satisfy both conditions simultaneously. $\newline$ Since we are looking for integers, we need to list the integers that are between $-3$ (not included) and $0$ (included).
List Satisfying Integers: List the integers that satisfy the conditions. $\newline$ The integers greater than $-3$ are $-2$ , $-1$ , $0$ , and so on. However, we are also limited by the condition that the integers must be less than or equal to $0$ . Therefore, the integers that satisfy both conditions are $-2$ , $-1$ , and $0$ .
Match with Choices: Match the set of integers found with the given choices. $\newline$ The set of integers that satisfy the conditions is $\{-2, -1, 0\}$ , which corresponds to choice (A).

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