Let R be the relation on Z defined by

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.

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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