Determining Candidate Keys
The previous example only illustrates the definition of a candidate key and not how these are determined in practice. It is important to determine all superkeys, which is especially difficult if the relation represents a set of relationships rather than a set of entities. Therefore it is often useful to attempt to find any "forgotten" superkeys by also determining the functional dependencies. We can derive more superkeys by applying the following rule:
- if S is a superkey and X→Y a functional dependency
- then (S ∖ {Y}) ∪ {X} is also a superkey, where '\' is the set difference.
Consider for example the relation
- Marriage (Husband, Wife, Date)
for which it will trivially hold that
- {Husband, Wife, Date}
is a superkey. If we assume that a certain person can marry at most once on a given date then this implies the functional dependencies:
- {Husband, Date} → Wife
- {Wife, Date} → Husband
In this case, applying the above rule leads to the derivation of the superkeys {Husband, Date} and {Wife, Date} respectively.
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