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.

Answer 1

The given relation is R={ ( a,b ):a,b∈Z,a−b  is an integer } .

It is known that the difference of integer is also an integer. So, ( a−b ) is also an integer.

The set of all first elements of the ordered pair in a relation R is called domain.

Domian of R=Z

The set of all second elements of the ordered pair in a relation R is called range.

Range of R=Z

Thus, the domain and range of the given relation is integers.