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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) $\{3, 4, 5, 6\}$ $\newline$ (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, 5\}

\newline

(B)

\{3, 4, 5\}

\newline

(C)

\{3, 4, 5, 6\}

\newline

(D)

\emptyset

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 Satisfying Integers: List the integers that satisfy the conditions. $\newline$ The integers greater than $2$ are $3, 4, 5, 6$ , and so on. However, we also need these integers to be less than $6$ . This excludes $6$ and any number greater than $6$ .
Combine Conditions: Combine the conditions to find the set of integers that are both greater than $2$ and less than $6$ . The only integers that satisfy both conditions are $3$ , $4$ , and $5$ . These are the integers that are greater than $2$ and less than $6$ .
Match with Choices: Match the set of integers found with the given choices. $\newline$ The set ${3, 4, 5}$ corresponds to choice $(B)$ .

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