# Superkey

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This article is about the programming term. For the keyboard button, see Super key (keyboard button).

A superkey is defined in the relational model of database organization as a set of attributes of a relation variable for which it holds that in all relations assigned to that variable, there are no two distinct tuples (rows) that have the same values for the attributes in this set.[1] Equivalently a superkey can also be defined as a set of attributes of a relation schema upon which all attributes of the schema are functionally dependent.

Note that the set of all attributes is a trivial superkey, because in relational algebra duplicate rows are not permitted.

Also note that if attribute set K is a superkey of relation R, then at all times it is the case that the projection of R over K has the same cardinality as R itself.

Informally, a superkey is a set of attributes within a table whose values can be used to uniquely identify a tuple. A candidate key is a minimal set of attributes necessary to identify a tuple, this is also called a minimal superkey. For example, given an employee schema, consisting of the attributes employeeID, name, job, and departmentID, we could use the employeeID in combination with any or all other attributes of this table to uniquely identify a tuple in the table. Examples of superkeys in this schema would be {employeeID, Name}, {employeeID, Name, job}, and {employeeID, Name, job, departmentID}. The last example is known as trivial superkey, because it uses all attributes of this table to identify the tuple.

In a real database we do not need values for all of those attributes to identify a tuple. We only need, per our example, the set {employeeID}. This is a minimal superkey – that is, a minimal set of attributes that can be used to identify a single tuple. So, employeeID is a candidate key.

## Example

English Monarchs
Monarch Name Monarch Number Royal House
Edward II Plantagenet
Edward III Plantagenet
Richard III Plantagenet
Henry IV Lancaster

First, list out all the (non-empty) sets of attributes:

• {Monarch Name}
• {Monarch Number}
• {Royal House}
• {Monarch Name, Monarch Number}
• {Monarch Name, Royal House}
• {Monarch Number, Royal House}
• {Monarch Name, Monarch Number, Royal House}

Second, eliminate all the sets which do not meet superkey's requirement. For example, {Monarch Name, Royal House} cannot be a superkey because for the same attribute values (Edward, Plantagenet), there are two distinct tuples:

• (Edward, II, Plantagenet)
• (Edward, III, Plantagenet)

Finally, after elimination, the remaining sets of attributes are the only possible superkeys in this example:

• {Monarch Name, Monarch Number} (Candidate Key)
• {Monarch Name, Monarch Number, Royal House}

In real situations, however, superkeys are normally not determined by this method, which is very tedious and time-consuming, but by analyzing functional dependencies.

## References

• Silberschatz, Abraham (2011). Database System Concepts (6th ed.). McGraw-Hill. pp. 45–46. ISBN 978-0-07-352332-3.
1. ^ Introduction to Database Management Systems. Tata McGraw-Hill. 2005. p. 77. ISBN 9780070591196. "no two tuples in any legal relation"