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Which is the set of integers greater than $2$ and less than $6$ ? $\newline$ Choices: $\newline$ (A) $\{3, 4, 5, 6\}$ $\newline$ (B) $\{3, 5\}$ $\newline$ (C) $\emptyset$ $\newline$ (D) $\{3, 4, 5\}$

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Set-builder notation

Full solution

Q. Which is the set of integers greater than

2

and less than

6

?

\newline

Choices:

\newline

(A)

\{3, 4, 5, 6\}

\newline

(B)

\{3, 5\}

\newline

(C)

\emptyset

\newline

(D)

\{3, 4, 5\}

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 $6$ . This means we need to find numbers that are between $2$ and $6$ , not including $2$ and $6$ themselves.
List Integers: List the integers that fall within this range. $\newline$ The integers greater than $2$ and less than $6$ are $3$ , $4$ , and $5$ . These are the only integers that satisfy both conditions.
Match Choices: Match the list of integers to the given choices. $\newline$ The list of integers we found in Step $2$ is $\{3, 4, 5\}$ . We need to find this set among the given choices.
Eliminate Incorrect Choices: Eliminate the incorrect choices. $\newline$ (A) includes the number $6$ , which should not be in the set because we are looking for numbers less than $6$ . $\newline$ (B) is missing the number $4$ , so it cannot be the correct set. $\newline$ (C) represents an empty set, which is not correct because there are integers that satisfy the conditions. $\newline$ (D) is the set \{ $3, 4, 5$ \}, which matches our list from Step $2$ .

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