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

Examples.

Inverse Relations

Composition of Relations