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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.

Solution:

Given R = {(a, b): a, b ∈ Z, a - b is an integer}
a ∈ Z
So, Domain of R is Z.
R is such that a - b ∈ Z and we have a ∈ Z so b ∈ Z.
So, Range of R is Z.
∴ Domain of R = Z and Range of R = Z.