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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) $\{3, 4, 5\}$ $\newline$ (D) $\emptyset$

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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)

\{3, 4, 5\}

\newline

(D)

\emptyset

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 all integers that fall between $2$ and $6$ , not including $2$ and $6$ themselves.
List Integers: List the integers that satisfy the conditions. $\newline$ The integers greater than $2$ and less than $6$ are $3$ , $4$ , and $5$ . These are the only integers that fit within the range specified by the 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. $\newline$ (A) $\{3, 4, 5, 6\}$ includes $6$ , which should not be included. $\newline$ (B) $\{3, 5\}$ is missing the integer $4$ . $\newline$ (C) $\{3, 4, 5\}$ matches our list exactly. $\newline$ (D) $\emptyset$ represents the empty set, which is not correct.
Select Correct: Select the correct choice based on the matching set. $\newline$ The correct choice is (C) $\{3, 4, 5\}$ because it is the set of integers that are greater than $2$ and less than $6$ .

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