Let `R` be the relation on `Z` defined by `R={(a , b): a , b in Z , a-b` is an integer`}dot` Find the domain and range of `Rdot`

Explanation

To find the domain and range of the relation \( R \) defined on \( \mathbb{Z} \) (the set of integers) by the condition \( R = \{(a, b) : a, b \in \mathbb{Z}, a - b \text{ is an integer}\} \), we can follow these steps:

### Step 1: Understand the Relation
The relation \( R \) consists of pairs \( (a, b) \) where both \( a \) and \( b \) are integers and the difference \( a - b \) is also an integer.

### Step 2: Identify the Domain
The domain of a relation consists of all possible first elements of the ordered pairs. In this case, since \( a \) can be any integer, the domain of \( R \) is:
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