Write the following statements in symbols :
the integers lying in between -3 and 2

Answer

To write the statement "the integers lying in between -3 and 2" in symbols, we can follow these steps:

### Step 1: Identify the range of integers
We need to find the integers that lie between -3 and 2. The integers in this range are -2, -1, 0, and 1.

### Step 2: Define the variable
Let’s denote the integers we are looking for as \( x \).

### Step 3: Set up the inequalities
Since we want \( x \) to be greater than -3 and less than 2, we can express this with inequalities:
- \( x > -3 \)
- \( x < 2 \)

### Step 4: Combine the inequalities
We can combine these inequalities into one statement:
- \( -3 < x < 2 \)

### Step 5: Specify that \( x \) is an integer
Since we are specifically looking for integers, we can add that \( x \) is an integer:
- \( x \in \mathbb{Z} \) (where \( \mathbb{Z} \) represents the set of all integers)

### Final Symbolic Representation
Putting it all together, we can write:
- \( -3 < x < 2 \) and \( x \in \mathbb{Z} \)

### Summary
The final symbolic representation of the integers lying between -3 and 2 is:
\[ -3 < x < 2, \quad x \in \mathbb{Z} \]

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