# Connected Relation

## Connected Relation

Relation defined in a set E so that, for every distinct pair of elements (x, y) of E, either one of the ordered pairs (xy) or (y, x) belong to the relation.

The arrow diagram of a connected relation in a set E includes at least one arrow between any two elements of E.

### Examples

• The relation “…is less than…” in a set of whole numbers is a connected relation.
Here is an arrow representation in the set E = [1, 2, 3, 4, 5}:

• The relation “…is greater than…” in a set of people is a connected relation.
• The relation “…is the same age as…” in a family is a disconnected relation.
• The relation “…is a multiple of…” in the set of whole numbers is a disconnected relation.