Question

What is the maximum number of super keys for the relation R1(P, Q, R, S) with R as the key

Answer 1

Explanation:

Any subset of attributes of a table that can uniquely identify all the tuples of that table is known as a Super key. Its different from the primary and candidate keys in the sense that only the minimal superkeys are the candidate/primary keys.

This means that from a super key when we remove all the attributes that are unnecessary for its uniqueness, only then it becomes a primary/candidate key. So, in essence, all primary/candidate keys are super keys but not all superkeys are primary/candidate keys. By the formal definition of a Relation(Table), we know that the tuples of a relation are all unique. So the set of all attributes itself is a super key.

Counting the possible number of superkeys for a table is a common question for GATE. The examples below will demonstrate all possible types of questions on this topic.

Example-1 : Let a Relation R have attributes {a1,a2,a3} & a1 is the candidate key. Then how many super keys are possible?

Here, any superset of a1 is the super key.

Super keys are = {a1, a1 a2, a1 a3, a1 a2 a3}

Thus we see that 4 Super keys are possible in this case.

Answer 2

Explanation:

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