ER model formulas

For an n-ary relationship set $R$ over entity sets $E_1,\dots ,E_n$. It holds because no two instances relate the same combination of entities. The bound is reached only when every combination is related.

In a binary 1:N relationship from A to B (each B related to at most one A), the count is at most $|B|$. With total participation of B it equals $|B|$. In a 1:1 relationship both sides are at-most-one, so $|R|\le \min (|A|,|B|)$.

Every entity of $E_i$ appears in at least one instance, and each instance contains exactly one entity of $E_i$.

Both bounds can be reached: the lower one by covering every entity with as few pairs as possible, the upper one by relating every pair.

The owner's key is copied in as a foreign key, normally declared ON DELETE CASCADE so that deleting an owner removes its weak entities. No separate relation is made for the identifying relationship.

Applies to a binary many-to-many relationship. Each key column is also a foreign key.

Counts recursive M:N relationship sets too. This is the count after merging every 1:1 and 1:N relationship (identifying relationships included) into an entity's relation. Each 1:1 relationship with total participation on both sides reduces the count by one more. Assumes no specialisation or aggregation.