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

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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)

\{3, 4, 5\}

\newline

(B)

\{3, 4, 5, 6\}

\newline

(C)

\{2, 3, 4, 5\}

\newline

(D)

\{2, 6\}

Define Inequality: Let's first define the inequality that represents the set of integers greater than or equal to $2$ and less than $6$ . We need to use two inequality signs: one for ＂greater than or equal to＂ ( $\geq$ ) and one for ＂less than＂ ( $<$ ).
Write Set Notation: Now, let's write down the set notation that includes all integers $x$ such that $2 \leq x < 6$ . This means we are looking for integers that are at least $2$ but strictly less than $6$ .
List Integers: We list out the integers that satisfy the inequality $2 \leq x < 6$ . These integers are $2$ , $3$ , $4$ , and $5$ . The number $6$ is not included because the inequality is strictly less than $6$ .
Match with Choices: We match our list of integers ${2, 3, 4, 5}$ with the given choices to find the correct set. $\newline$ (A) ${3, 4, 5}$ does not include $2$ , so it is not correct. $\newline$ (B) ${3, 4, 5, 6}$ includes $6$ , which should not be in the set, so it is not correct. $\newline$ (C) ${2, 3, 4, 5}$ includes all the integers that satisfy the inequality, so it is correct. $\newline$ (D) ${2, 6}$ does not include $3$ , $4$ , or $5$ , so it is not correct.

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