Question

Define a relation on a set. What do you mean by the domain and range of a relation. Give an example.

Answer 1

A relation R in a set A is a subset of A × A.

Thus, R is a relation in a set A R ⊆ A × A.

If (a, b) ∈ R then we say that a is related to b and write, a R b.

If (a, b) ∉ R then we say that a is not related to b and write, a Ꞧ b.

Consider R be a relation in a set A. Then, the set of all first coordinates of elements of R is called the domain of R, written as dom (R) and the set of all second coordinates of R is called the range of R, written as range (R).

For example:

R = {(-1, 1), (1, 1), (-2, 4), (2, 4)}

dom (R) = {-1, 1, -2, 2}

range (R) = {1, 4}