Relations

Definitions

• Cartesian Product of sets
  

• Ordered pair
  

Relation

Let . A relation is a non-empty subset of .

• Domain of :
• Codomain of :
• Range of :
• Pre-range of :

Everywhere defined

is everywhere defined

.

Onto

is onto

Aka. surjection.

Inverse

Inverse of :

Types of relation

one-many

Not one-many

many-one

Not many-one

many-many

iff is one-many and many-one.

one-one

iff is not one-many and not many-one. Aka. injection.

Bijection

When a relation is onto and one-one.