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

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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\}

\newline

(B)

\emptyset

\newline

(C)

\{3, 5\}

\newline

(D)

\{3, 4, 5, 6\}

Identify Range: Identify the range of integers that satisfy the condition. $\newline$ We are looking for integers that are greater than $2$ and less than $6$ . This means we need to find all integers that fall between $2$ and $6$ , not including $2$ and $6$ themselves.
List Integers: List the integers that satisfy the condition. $\newline$ The integers greater than $2$ and less than $6$ are $3$ , $4$ , and $5$ . These are the only integers that fit within the given range.
Match Choices: Match the list of integers to the given choices. $\newline$ The list of integers we found in Step $2$ is $\{3, 4, 5\}$ . Now we need to find which choice corresponds to this set. $\newline$ (A) $\{3, 4, 5\}$ matches our list. $\newline$ (B) $\emptyset$ is the empty set and does not match. $\newline$ (C) $\{3, 5\}$ is missing the integer $4$ and does not match. $\newline$ (D) $\{3, 4, 5, 6\}$ includes $6$ , which should not be in the set as it is not less than $6$ .

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