Editing Domain relational calculus (section)

==Examples==
Let (A, B, C) mean (Rank, Name, ID) in the Enterprise relation

and let (D, E, F) mean (Name, DeptName, ID) in the Department relation

All captains of the starship [[USS Enterprise (NCC-1701)|USS Enterprise]]:
<math display="block">\left\{ \ {\left\langle A, B, C \right\rangle} \mid {\left\langle A, B, C \right\rangle \in \mathrm{Enterprise} \ \land \ A = \mathrm{'Captain'} } \ \right\}</math>

In this example, A, B, C denotes both the result set and a set in the table Enterprise.

Names of Enterprise crew members who are in Stellar Cartography:
<math display="block">\begin{align}
\{ {\left\langle B \right\rangle}
& \mid {\exists A, C \ \left\langle A, B, C \right\rangle \in \mathrm{Enterprise} } \\
& \land \ {\exists D, E, F \ \left\langle D, E, F \right\rangle \in \mathrm{Departments} } \\
& \land \ F = C \\
& \land \ E = \mathrm{'Stellar\ Cartography'} \} \\
\end{align}</math>

In this example, we're only looking for the name, and that's B.  The condition F = C is a requirement that describes the intersection of Enterprise crew members AND members of the Stellar Cartography Department.

An alternate representation of the previous example would be:
<math display="block">\begin{align}
\{ {\left\langle B \right\rangle}
& \mid {\exists A, C \ \left\langle A, B, C \right\rangle \in \mathrm{Enterprise} } \\
& \land \ {\exists D \ \left\langle D, \mathrm{'Stellar\ Cartography'}, C \right\rangle \in \mathrm{Departments} } \} \\
\end{align}</math>

In this example, the value of the requested F domain is directly placed in the formula and the C domain variable is re-used in the query for the existence of a department, since it already holds a crew member's ID.

Both of them written in [[SQL]] will be like:<syntaxhighlight lang="sql">
SELECT B
FROM Enterprise
JOIN Department
  ON F = C
 AND E = 'Stellar Cartography';
</syntaxhighlight>