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

\newline

(B)

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

\newline

(C)

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

\newline

(D)

\{0, 1\}

Identify Inequality Signs: Let's first identify the inequality signs. We need to find the set of integers that are greater than $-4$ and less than or equal to $1$ . The inequality signs we are looking for are: $>$ for greater than and $\leq$ for less than or equal to.
Translate to Set Notation: Now, let's translate the inequalities into set notation. The set notation for integers greater than $-4$ and less than or equal to $1$ is: $\{x \,|\, -4 < x \leq 1\}$ .
List Integers in Range: Next, we need to list the integers that satisfy the inequality $-4 < x \leq 1$ . Remember that integers are whole numbers, so we need to list the whole numbers in this range. $\newline$ The integers greater than $-4$ are $-3, -2, -1, 0, 1, 2, 3,$ ... and so on. $\newline$ However, we are only interested in those less than or equal to $1$ .
Match with Given Choices: Listing the integers that satisfy both conditions, we get: $-3$ , $-2$ , $-1$ , $0$ , $1$ . These are the integers that are greater than $-4$ and less than or equal to $1$ .
Match with Given Choices: Listing the integers that satisfy both conditions, we get: $-3, -2, -1, 0, 1$ . These are the integers that are greater than $-4$ and less than or equal to $1$ . Now, let's match our set of integers with the given choices. (A) $\{-4, 0, 1\}$ includes $-4$ , which is not greater than $-4$ . (B) $\{-4, -3, -2, -1, 0, 1\}$ also includes $-4$ , which is not greater than $-4$ . (C) $\{-3, -2, -1, 0, 1\}$ does not include $-4$ and includes all integers from $-4$ $1$ to $1$ , which satisfies our condition. (D) $-4$ $3$ does not include all integers greater than $-4$ and less than or equal to $1$ .

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