Cardinality of Relationships

Cardinality is the number of entity instances to which another entity set can map under the relationship. This does not reflect a requirement that an entity has to participate in a relationship. Participation is another concept.
One-to-one: X-Y is 1:1 when each entity in X is associated with at most one entity in Y, and each entity in Y is associated with at most one entity in X.
One-to-many: X-Y is 1:M when each entity in X can be associated with many entities in Y, but each entity in Y is associated with at most one entity in X.
Many-to-many: X:Y is M:M if each entity in X can be associated with many entities in Y, and each entity in Y is associated with many entities in X (“many” =>one or more and sometimes zero)