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

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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, 0\}

\newline

(C)

\{-2, -1\}

\newline

(D)

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

Identify Range of Integers: Let's first identify the range of integers we are looking for. We need to find the set of integers that are greater than $-3$ and at the same time less than or equal to $0$ .
List Whole Numbers: We know that integers are whole numbers, so we need to list the whole numbers that are between $-3$ (not included, since it's strictly greater than $-3$ ) and $0$ (included, since it's less than or equal to $0$ ).
Count Up to $0$ : Starting from $-2$ (the first integer greater than $-3$ ), we count up to $0$ . The integers in this range are $-2$ , $-1$ , and $0$ .
Match with Choices: Now, let's match our set of integers with the given choices. The set $\{-2, -1, 0\}$ corresponds to choice (B).

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