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

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Set-builder notation

Full solution

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

-1

and less than

4

?

\newline

Choices:

\newline

(A)

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

\newline

(B)

\{0, 1, 2, 3\}

\newline

(C)

\{-1, 0, 1, 2, 3\}

\newline

(D)

\{-1, 0, 2, 3\}

Identify Inequality Signs: Identify the inequality signs and the range of integers needed. $\newline$ We are looking for integers that are greater than or equal to $-1$ and less than $4$ . $\newline$ The inequality signs we are using are $\geq$ for greater than or equal to, and $<$ for less than.
List Integers: List the integers that satisfy the first part of the condition, which is greater than or equal to $-1$ . $\newline$ The integers greater than or equal to $-1$ are: $-1$ , $0$ , $1$ , $2$ , $3$ , $4$ , $5$ , and so on.
Apply Second Condition: Now, apply the second part of the condition, which is less than $4$ . From the list in Step $2$ , the integers less than $4$ are: $-1$ , $0$ , $1$ , $2$ , $3$ .
Combine Conditions: Combine both conditions to find the set of integers that are both greater than or equal to $-1$ and less than $4$ . $\newline$ The set of integers that satisfy both conditions is: $\{-1, 0, 1, 2, 3\}$ .
Match with Choices: Match the set we found with the given choices. $\newline$ The set ${-1, 0, 1, 2, 3}$ matches with choice $(C)$ .

More problems from Set-builder notation

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