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If $\text{D}_1,\text{D}_2, \dots \text{D}_n$ are domains in a relational model, then the relation is a table, which is a subset of

  1. $\text{D}_1 \oplus \text{D}_2 \oplus \dots \oplus \text{D}_n$
  2. $\text{D}_1 \times \text{D}_2 \times \dots \times \text{D}_n$
  3. $\text{D}_1 \cup \text{D}_2 \cup \dots \cup \text{D}_n$
  4. $\text{D}_1 \cap \text{D}_2 \cap \dots \cap \text{D}_n$
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Given sets $D_{1}, \  D_{2}, \  …, \  D_{n} $ not necessarily distinct.

The Cartesian product $D_{1}XD_{2}X.....XD_{n}$ is the set of all (ordered) $n-tuples$  $< d_{1}, \ d_{2}, \ d_{3}, \ ....... \, \ d_{n} >$   such that $d_{1} \ \epsilon \ D_{1} , \ d_{2} \ \epsilon \ D_{2} \ ..........., \ d_{n} \ \epsilon \ D_{n}$

A mathematical relation on $D_{1}, \  D_{2}, \  …, \  D_{n} $ is a subset of the Cartesian product $D_{1}XD_{2}X.....XD_{n}$

$D_{1}, \  D_{2}, \  …, \  D_{n} $ are the domains of the relations.

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