If `R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z}` is a relation on `Z` , write the domain of `R` .

Explanation

To find the domain of the relation \( R = \{(x, y) : x^2 + y^2 \leq 4; x, y \in \mathbb{Z}\} \), we need to determine the possible integer values of \( x \) such that there exists an integer \( y \) satisfying the condition \( x^2 + y^2 \leq 4 \).

### Step-by-Step Solution:

1. **Understand the Condition**: The relation states that \( x^2 + y^2 \) must be less than or equal to 4. This describes a circle of radius 2 centered at the origin in the coordinate plane.

2. **Determine Possible Values for \( y \)**: Since \( y \) is also an integer, we need to find the maximum possible values for \( y \) given different integer values of \( x \).

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