Superkey

In the relational data model a superkey is any set of attributes that uniquely identifies each tuple of a relation. Because superkey values are unique, tuples with the same superkey value must also have the same non-key attribute values. That is, non-key attributes are functionally dependent on the superkey.

The set of all attributes is always a superkey (the trivial superkey). Tuples in a relation are by definition unique, with duplicates removed after each operation, so the set of all attributes is always uniquely valued for every tuple. A candidate key (or minimal superkey) is a superkey that can't be reduced to a simpler superkey by removing an attribute.

For example, in an employee schema with attributes,  ,  , and  , if   values are unique then   combined with any or all of the other attributes can uniquely identify tuples in the table. Each combination, { }, {, }, { ,  ,  }, and so on is a superkey. { } is a candidate key, since no subset of its attributes is also a superkey. {, ,  ,  } is the trivial superkey.

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.

Example
First, list out all the 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} — this is also the candidate key
 * {Monarch Name, Monarch Number, Royal House}

In reality, superkeys cannot be determined simply by examining one set of tuples in a relation. A superkey defines a functional dependency constraint of a relation schema which must hold for all possible instance relations of that relation schema.