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

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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)

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

\newline

(B)

\{-4, 0, 1\}

\newline

(C)

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

\newline

(D)

\{0, 1\}

Identify Inequality: Identify the inequality that represents the set of integers greater than $-4$ and less than or equal to $1$ . The inequality for greater than $-4$ is $x > -4$ , and the inequality for less than or equal to $1$ is $x \leq 1$ . We need to find the intersection of these two inequalities.
Determine Integers: Determine the set of integers that satisfy both inequalities. $\newline$ Since we are looking for integers, we need to list the integers that are greater than $-4$ and at the same time less than or equal to $1$ . The integer immediately greater than $-4$ is $-3$ .
List Integers: List all the integers between $-3$ and $1$ inclusive. $\newline$ The integers that satisfy both conditions are $-3$ , $-2$ , $-1$ , $0$ , and $1$ .
Match Choices: Match the list of integers with the given choices. $\newline$ The correct set of integers is $\{-3, -2, -1, 0, 1\}$ , which corresponds to choice $(C)$ .

More problems from Set-builder notation

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1

\newline

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