Operations on Relations

In this class, We discuss Operations on Relations.

The reader should have prior knowledge of Introduction to Relations. Click here.

Operations:

1) Union

2) Intersection

3) Difference

4) Symmetric difference

Let A and B be two relations.

x (A ∪ B) y = x A y or x B y

x (A ∩ B) y = x A y and x B y

x (A – B) y = x A y and x not B y

x (A + B) y = x (A ∪ B) y – x (A ∩ B) y

Examples:

A = {(1,2), (2, 4), (3, 3))

B = {(1,3}, {2,4},(4,2)}

x (A ∪ B) y = {(1,2), (1, 3), (2, 4), (3, 3), (4,2)}

x (A ∩ B) y = {(2, 4)}

x (A – B) y = {(1,2), (3, 3)}

x (A + B) y = {(1,2), (1, 3), (3, 3), (4,2)}