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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) $\{-3, 0\}$ $\newline$ (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)

\{-2, -1, 0\}

\newline

(B)

\{-2, -1\}

\newline

(C)

\{-3, 0\}

\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 less than or equal to $0$ .
Consider Inequality for Range: Now, let's consider the inequality that represents this range. The inequality for numbers greater than $-3$ is $x > -3$ , and for numbers less than or equal to $0$ is $x \leq 0$ . We need to find the intersection of these two sets.
List Whole Numbers: We know that integers are whole numbers, so we need to list the whole numbers that satisfy both conditions. The smallest integer greater than $-3$ is $-2$ , and the largest integer less than or equal to $0$ is $0$ itself.
Find Integers that Satisfy: Listing out the integers that satisfy both conditions, we get $-2$ , $-1$ , and $0$ . These are the integers that are greater than $-3$ and less than or equal to $0$ .
Match with Given Choices: Looking at the choices given, we can see that the set of integers that matches our list is $\{-2, -1, 0\}$ .

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