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Question

Let R be the relation on Z defined by
R = {(a, b) : a, b ∈ Z, a − b is an integer}
Find the domain and range of R.

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Solution

R = {(a, b) : a, b ∈ Z, a − b is an integer}
We know:
Difference of any two integers is always an integer.
Thus, for all a, b ∈ Z, we get a − b as an integer.
∴ Domain (R) = Z
And,
Range (R) = Z

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