Union of Relations

The union of two relations means combining all ordered pairs from the relations. The result is a new relation that contains every connection that is in at least one of the relations.

Formal Definition

In the union, we simply 'add' the relations: any connection that appeared in either is in the new relation.

Examples of Union of Relations

Let A = {1,2,3}, R = { (1,2), (2,3) }, S = { (2,3), (3,1) }.

Then R ∪ S = { (1,2), (2,3), (3,1) }.

Properties

• The union always includes all pairs from both relations.
• The union is commutative: R ∪ S = S ∪ R.
• The union is associative: (R ∪ S) ∪ T = R ∪ (S ∪ T).
• The union generally does not preserve relation properties (e.g., the union of two partial orders may not remain a partial order).

Summary

The union of relations creates a new relation that combines all connections from the original relations. This is useful when we want to handle different connections together, for example in kinship or transportation networks.

Practice Exercise