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

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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)

\{-3, 0\}

\newline

(B)

\{-2, -1\}

\newline

(C)

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

\newline

(D)

\{-2, -1, 0\}

Identify Range: Identify the range of integers that satisfy the given conditions. $\newline$ We are looking for integers that are greater than $-3$ and less than or equal to $0$ . This means we need to find all integers that fall between $-3$ (not included) and $0$ (included).
List Integers: List the integers that satisfy the conditions. $\newline$ Starting from $-3$ and moving towards $0$ , the integers that are greater than $-3$ are $-2$ , $-1$ , $0$ . We do not include $-3$ because the condition is ＂greater than $-3$ ,＂ not ＂greater than or equal to $-3$ .＂
Check Choices: Check the choices given to see which one matches our list. $\newline$ (A) $\{-3, 0\}$ includes $-3$ , which should not be included. $\newline$ (B) $\{-2, -1\}$ does not include $0$ , which should be included. $\newline$ (C) $\{-3, -2, -1, 0\}$ includes $-3$ , which should not be included. $\newline$ (D) $\{-2, -1, 0\}$ matches our list of integers that are greater than $-3$ and less than or equal to $0$ .

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