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Which is the set of integers greater than $-4$ and less than or equal to $1$ ? $\newline$ Choices: $\newline$ (A) $\{0, 1\}$ $\newline$ (B) $\{-3, -2, -1, 0, 1\}$ $\newline$ (C) $\{-4, 0, 1\}$ $\newline$ (D) $\{-4, -3, -2, -1, 0, 1\}$

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Set-builder notation

Full solution

Q. Which is the set of integers greater than

-4

and less than or equal to

1

?

\newline

Choices:

\newline

(A)

\{0, 1\}

\newline

(B)

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

\newline

(C)

\{-4, 0, 1\}

\newline

(D)

\{-4, -3, -2, -1, 0, 1\}

Identify Inequality Condition: Identify the inequality that represents the condition ＂greater than $-4$ and less than or equal to $1$ ＂. $\newline$ The inequality for this condition is $-4 < x \leq 1$ , where $x$ is an integer.
Determine Satisfying Integers: Determine the set of integers that satisfy the inequality $-4 < x \leq 1$ . The integers greater than $-4$ are $-3, -2, -1, 0, 1, 2, 3, \ldots$ However, we also need to consider that $x$ must be less than or equal to $1$ . Therefore, we exclude any integers greater than $1$ .
List Satisfying Integers: List the integers that satisfy both conditions. $\newline$ The integers that are greater than $-4$ and less than or equal to $1$ are: $-3$ , $-2$ , $-1$ , $0$ , $1$ .
Match with Choices: Match the set of integers from Step $3$ with the given choices. $\newline$ The correct set of integers is $(B)\{-3, -2, -1, 0, 1\}$ .

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