Relationship

If A and B are sets, then a relation R is a subset of A * B

Relationship

One-to-one
One-to-many; Many-to-one
Many-to-many

Relationship 1

Multiplicity & Cardinality

In UML, multiplicity specifies lower and upper bound constraints on the cardinality of a relationship

Multiplicity	Cardinality	Description
0..0	0	Collection must be empty
0..1		Either zero or one instance
1..1	1	Exactly one instance
0..*	*	Zero or more instances
1..*		One or more instance
5..5	5	Exactly 5 instances
m..n		At least m, but no more than n instances

Multi-way Relationships

relation

A and B are two sets (collections of things).

Example:
A = {Person1, Person2}
B = {Product1, Product2}

A × B (called the "Cartesian product") is all possible combinations of one item from A and one item from B.
A × B = { (Person1, Product1), (Person1, Product2), (Person2, Product1), (Person2, Product2) }

Relation R is some subset of A × B — meaning R just picks certain pairs out of A × B that actually make sense for the relationship you're modeling.

relation1