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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) $\{-4, 0, 1\}$ $\newline$ (C) $\{-3, -2, -1, 0, 1\}$ $\newline$ (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)

\{-4, 0, 1\}

\newline

(C)

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

\newline

(D)

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

Identify Inequality Signs: Let's first identify the inequality signs and the type of numbers we are dealing with. We are looking for integers that are greater than $-4$ and less than or equal to $1$ .
List Type of Numbers: The inequality greater than $-4$ is represented by the symbol $>$ , and the inequality less than or equal to $1$ is represented by the symbol $\leq$ . So we are looking for integers $x$ such that $-4 < x \leq 1$ .
Find Integers: Now we need to list the integers that satisfy both conditions. The smallest integer greater than $-4$ is $-3$ , and the largest integer that is less than or equal to $1$ is $1$ itself.
List Integers: Listing out the integers between $-3$ and $1$ inclusive, we get $-3, -2, -1, 0, 1$ . These are the integers that satisfy the condition $-4 < x \leq 1$ .
Compare Choices: Comparing our list with the given choices, we find that choice (C) $\{ -3, -2, -1, 0, 1 \}$ matches our list.

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