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Which is the set of integers greater than or equal to $0$ and less than or equal to $6$ ? $\newline$ Choices: $\newline$ (A) $\{1, 2, 3, 4, 5, 6\}$ $\newline$ (B) $\{0, 1, 2, 3, 4, 5, 6\}$ $\newline$ (C) $\{1, 6\}$ $\newline$ (D) $\emptyset$

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Set-builder notation

Full solution

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

0

and less than or equal to

6

?

\newline

Choices:

\newline

(A)

\{1, 2, 3, 4, 5, 6\}

\newline

(B)

\{0, 1, 2, 3, 4, 5, 6\}

\newline

(C)

\{1, 6\}

\newline

(D)

\emptyset

Identify Inequality Signs: Identify the inequality signs for the problem. We need to find the set of integers that are greater than or equal to $0$ and less than or equal to $6$ . The inequality signs we are looking for are ＂greater than or equal to＂ ( $\geq$ ) and ＂less than or equal to＂ ( $\leq$ ).
Translate to Set Notation: Translate the inequalities into set notation. The set notation for integers greater than or equal to $0$ and less than or equal to $6$ is $\{x \,|\, 0 \leq x \leq 6\}$ .
List Satisfying Integers: List the integers that satisfy the inequality $0 \leq x \leq 6$ . These integers are $0$ , $1$ , $2$ , $3$ , $4$ , $5$ , and $6$ .
Match with Choices: Match the list of integers with the given choices to find the correct set. $\newline$ (A) $\{1, 2, 3, 4, 5, 6\}$ does not include $0$ , so it is not the correct set. $\newline$ (B) $\{0, 1, 2, 3, 4, 5, 6\}$ includes all integers from $0$ to $6$ , so it is the correct set. $\newline$ (C) $\{1, 6\}$ only includes $1$ and $6$ , so it is not the correct set. $\newline$ (D) $\emptyset$ represents the empty set, which is not the correct set since there are integers that satisfy the inequality.

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