Foreign Key (Databases)

A foreign key is a set of attributes $F K$ in a relation schema $R_{1}$ , that references a relation $R_{2}$ if it satisfies the following rules:

Attributes in the $F K$ must have the same domain(s) as the primary key attributes $P K$ , the attributes are said to refer to the relation $R_{2}$ .
A value of $F K$ in tuple $t_{1}$ of $r_{1} (R_{1})$ either occurs as a value of $P K$ for some tuple $t_{2}$ in the relation state $r_{2} (R_{2})$ or it is null. $t_{1} [F K] = t_{2} [P K]$ In the case that the value of the $F K$ on $R_{1}$ is null, it should not be part of its own primary key.

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