Discrete Mathematical Structures by Pearson

Relations and Digraphs 2-3

Example 2 Let A = {1, 2, 3, 4}, B = {x, y, z, p, q}, and R = {(1, x), (2, y), (3, p)}

Then, Dom (R) = {1, 2, 3} and Range (R) = {x, y, p}

2.2.2 Types of Relations

Inverse Relation: Let R be any relation from a set A to a set B. The inverse relation denoted by

R

−1

is the relation from B to A defined by,

R

−1

= {(b, a): (a, b) ∈ R}

that is, the inverse relation is obtained by interchanging the order in each ordered pair of R.

(a, b) ∈ R ⇔ (b, a) ∈ R

−1

The Dom (R) = Range (R

−1

) and vice versa.

For example: Let the relation R from A = {2, 3, 5} to B = {4, 7, 9}

defined by R = {(2, 4), (3, 7), (5, 9)}, then R

−1

= {(4, 2), (7, 3), ...