I did not understand the solution here can someone explain it to me (1) Relation

Question

I did not understand the solution here can someone explain it to me

(1) Relation R(A,B,C,D,E) has exactly four superkeys. Can you deduce from this statement the number of candidate keys? If yes, how many CK are there? Justify your answer.

Solution:

No. If ABC is the only CK of R, then there are four superkeys: ABC, ABCD, ABCE and ABCDE. On the other hand, if there are three CKs: ABCD, ABCE and ABDE, there are also four superkeys: ABCD, ABCE, ABDE and ABCDE.

(2) A relation R of four attributes has two candidate keys, what are the maximum and minimum numbers of superkeys R may have?

Solution:

Minimum: 3; e.g. when the candidate keys are ABC and ABD.
Maximum: 12; e.g. when the candidate keys are A and B.

Explanation / Answer

First you need to understand what are keys?

Candidate key: it is a key with which we can uniquely find a tuple in a relation. These keys are candidates for Primary key.

Super key: if we add attributes in a CK, then it will become superkey.

Now, Q1.) We can't deduce the number of CKs if there are 4 superkeys. Example is already provided.

Q2.) If we have 2 CKs then we can have minimum of 3 superkeys as CK need to be unique and with 4 attributes, we can have 2 candidate key of 3 attributes.

For maximum number of Superkeys, we have CKs with 1 attribute and that will give us 12 Superkeys.

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