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

\newline

(B)

\{3, 4, 5\}

\newline

(C)

\emptyset

\newline

(D)

\{3, 4, 5, 6\}

Identify Range of Integers: 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 Greater Than $2$ : List the integers that are greater than $2$ . The integers greater than $2$ are $3$ , $4$ , $5$ , $6$ , $7$ , and so on. However, we are also constrained by the condition that the integers must be less than $6$ .
List Less Than $6$ : List the integers that are less than $6$ . $\newline$ The integers less than $6$ are ... $-1, 0, 1, 2, 3, 4, 5$ . We need to find the intersection of the integers greater than $2$ and less than $6$ .
Find Intersection: Find the intersection of the two sets from Step $2$ and Step $3$ . $\newline$ The intersection of the integers greater than $2$ and less than $6$ is the set $\{3, 4, 5\}$ .
Match with Choices: Match the set from Step $4$ with the given choices. $\newline$ The set ${3, 4, 5}$ matches with choice $(B)$ .

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