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

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Set-builder notation

Full solution

Q. Which is the set of integers greater than or equal to

2

and less than

6

?

\newline

Choices:

\newline

(A)

\{2, 6\}

\newline

(B)

\{2, 3, 4, 5\}

\newline

(C)

\{3, 4, 5, 6\}

\newline

(D)

\{3, 4, 5\}

Identify Inequality Signs: Let's first identify the inequality signs for the set of integers we are looking for. We need to find the set of integers that are greater than or equal to $2$ and also less than $6$ . $\newline$ Inequality signs: $\geq$ for greater than or equal to, and $<$ for less than.
Translate to Set Notation: Now, let's translate the inequality into set notation. The set notation for integers greater than or equal to $2$ and less than $6$ is $\{x \,|\, 2 \leq x < 6\}$ .
List Integers: Next, we need to list out the integers that satisfy the inequality $2 \leq x < 6$ . These integers are $2$ , $3$ , $4$ , and $5$ .
Match with Choices: Finally, let's match our set of integers $\{2, 3, 4, 5\}$ with the given choices to find the correct answer. $\newline$ (A) $\{2, 6\}$ does not include all the integers between $2$ and $6$ and includes $6$ which should not be included. $\newline$ (B) $\{2, 3, 4, 5\}$ includes all the integers between $2$ and $6$ , excluding $6$ , which is correct. $\newline$ (C) $\{3, 4, 5, 6\}$ does not include $2$ and includes $6$ which should not be included. $\newline$ (D) $\{2, 6\}$ $2$ does not include $2$ which should be included.

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