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

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Set-builder notation

Full solution

Q. Which is the set of integers greater than

-2

and less than

1

?

\newline

Choices:

\newline

(A)

\{-1, 0, 1\}

\newline

(B)

\emptyset

\newline

(C)

\{-1, 0\}

\newline

(D)

\{-2, -1, 0\}

Identify Range: Identify the range of integers that satisfy the given conditions. $\newline$ We are looking for integers that are greater than $-2$ and less than $1$ . This means we need to find integers that are between $-2$ and $1$ , but not including $-2$ and $1$ themselves.
List Integers: List the integers that fall within the range. $\newline$ The integers greater than $-2$ are $-1$ , $0$ , $1$ , $2$ , and so on. However, we also need these integers to be less than $1$ . This excludes $1$ and any integer greater than $1$ .
Identify Set: Identify the correct set from the given choices. $\newline$ From the integers listed in Step $2$ , we can see that only $-1$ and $0$ satisfy both conditions: they are greater than $-2$ and less than $1$ . Therefore, the correct set of integers is \{ $-1$ , $0$ \}.

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