## Math 3000 - Lectures 11 & 12

### Relations

** Def**: *Ordered pair* (a,b) = { {a},{a,b} }.
** Def**: *Cartesian product* - set of all ordered pairs.

**Def**: *Indexed Sets* (A family of sets is a set whose members are sets)

A *relation on a set* is a subset of the cartesian product of the set with itself.

A *relation between two sets* is a subset of the cartesian product of the two sets.

*Cartesian graph* of a relation.

*Domain* and *Range* of a relation.

*Identity Relation*

#### Properties of Relations

- Reflexive
- Symmetric
- Transitive
- Antisymmetric

Examples.
Inverse Relations

Composition of Relations