Question

Write the following set in roster form and in​ set-builder notation.
N is the set of integers that are greater than or equal to negative 2 and less than 2.
Question content area bottom
Part 1
Write the set in roster form.
Nequals​{
  
negative 2,negative 1,0,1​}
​(Use a comma to separate answers as​ needed.)
Part 2
Write the set in​ set-builder notation. Choose the correct answer below.
A.
Nequals​{x ​| x is an​ integer, xgreater thannegative 2​, xless than2​}
B.
Nequals​{x ​| x is an​ integer, xgreater thannegative 2​, xless than or equals2​}
C.
Nequals​{x ​| x is an​ integer, xgreater than or equalsnegative 2​, xless than2​}
D.
Nequals​{x ​| x is an​ integer, xgreater than or equalsnegative 2​, xless than or equals2​}

Answer 1

Let's break down the question in two parts as you requested.

### Part 1: Roster Form
The set \( N \), which consists of integers that are greater than or equal to \(-2\) and less than \(2\), can be written in roster form as:
\[
N = \{-2, -1, 0, 1\}
\]

### Part 2: Set-Builder Notation
For set-builder notation, we want to express the same conditions: integers that are greater than or equal to \(-2\) and less than \(2\). The correct option is:

**C.** \( N = \{ x \mid x \text{ is an integer}, -2 \leq x < 2 \} \)

This option accurately describes the set using the specified conditions.

Thus, the answers are:
- **Roster Form:** \( N = \{-2, -1, 0, 1\} \)
- **Set-Builder Notation:** Option C: \( N = \{ x \mid x \text{ is an integer}, -2 \leq x < 2 \} \)