Representing Relations Table and Graph

In this class, We discuss the Representing Relations Table and Graph.

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

Relation matrix:

A = {1, 2, 3, 4}

B = {b1, b2, b3}

R = {(1, b2), (1, b3), (3, b2), (4, b3)}

The below diagram shows the matrix representation of relations.

We place 1 when a relation is present—otherwise 0.

Example 2:

A = {1, 2, 3, 4}

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

The diagram below shows the matrix representation.

Representing relations using a graph.

aRb or (a,b)

The diagram below shows the graph for aRb.

aRa, aRb ∩ bRa, aRb ∩ bRc ∩ cRa

The diagrams below show the relations.

Example:

A = {5, 6, 7, 8}

R = {(8, 5), (8, 6), (8, 7), (7, 5), (7, 6), (6, 5)}

The below diagram shows the graph.