The set A= {x:x is an integer and `-3lexlt2}` is equal to :

Options

A. `phi`
B. `{-3,-2,-1,0,1}`
C. `{-3,-2-1,0,1,2}`
D. None of these.

Answer

To solve the problem, we need to express the set \( A = \{ x : x \text{ is an integer and } -3 \leq x < 2 \} \) in roster form. Let's go through the steps:

### Step 1: Identify the range of integers
The condition given is that \( x \) is an integer between -3 and 2. The inequality states that \( x \) can take values starting from -3 (inclusive) up to 2 (exclusive).

### Step 2: List the integers starting from -3
Since -3 is included in the set, we start listing integers from -3:
- The first integer is -3.

### Step 3: Continue listing integers up to but not including 2
Next, we continue to list the integers:
- After -3, the next integer is -2.
- Then -1.
- Then 0.
- Then 1.

### Step 4: Stop before reaching 2
Since the inequality does not include 2, we stop listing integers before we reach 2. Therefore, we do not include 2 in our set.

### Final Result
Now, we can write the set \( A \) in roster form:
\[ A = \{-3, -2, -1, 0, 1\} \]