number of superkey

Question

consider the following relational schema R(ABCDE) .The number of  super keys in relation R if every two attributes of relation R is candidate keys are ___________

Comments

R(ABCDE) every 2 elements are candidate keys, 5C2 = 10 CKs possible

any supperset of CKis SK. so SKs will be

5C2 + 5C3 + 5C4 + 5C5 = 10 + 10 + 5 + 1 = 26 SKs

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@Manu i do not get concept how you solve this question can you please, elaborate it a little bit more.

Answer 1

Here in question it is given that combination of every two attributes is candidate key.So different combination of 2 attribute possible is $\binom{5}{2}$ i.e 10(AB,AC,AD,AE,BC,BD,BE,CD,CE,DE).

 Total subset of {A,B,C,D,E} is 2^5-1(for phi)=31.

All the subset will definitely be super key accept those with single element i.e {A},{B},{C},{D},{E}.

Now the remaining subset will be of length 2 or 3 or 4 and they will definitely contain the combination of two attribute or more than it .

For eg:-{A,B},{B,C}.............{A,B,C},{B,C,D}....... and so on .......

So the only 5 possible singleton subset are not super key .All other are super key .

31-5=26.

Comments

grt approche thnk you . i do same problem with another approch but it is very lengthy