Made easy self dought

Question

Q. R(A,B,C,D,E,F) with {A,BC,CD} candidate keys.How many super keys possible?

Comments

My answer is 48 . It is true?

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$$|\{A, AF, AE, AEF, BC, BCF, BCE, BCEF, CS, CDF, CDE, CDEF, ABC, ABCF, ABCE, ABCEF, ACD, ACDF, ACDE, ACDEF, ABCD, ABCDF, ABCDE, ABCDEF\}| = 24$$

How 48? I am getting 24.

Answer 1

We can solve it using Inclusion-Exclusion principle.

Let “a” denote set of all super keys which have “A” as one of the attributes.

Let “bc” denote set of all super keys which have “BC” as two of the attributes.

Let “cd” denote set of all super keys which have “CD” as two of the attributes.

Now, our answer to “number of super keys” will be :

$a \cup bc \cup cd = |a| + |bc| + |cd| – |abc| – |acd| – |bcd| + |abcd| $

$|a| = 2^5 ; |bc| = 2^4 ; |cd| = 2^4 ; |abc| = 2^3 ; |acd| = 2^3 ; |bcd| = 2^3 ; |abcd| = 2^2$

$a \cup bc \cup cd = 44 $

So, answer is 44.

Comments

$$|\{A, AF, AE, AEF, BC, BCF, BCE, BCEF, CS, CDF, CDE, CDEF, ABC, ABCF, ABCE, ABCEF, ACD, ACDF, ACDE, ACDEF, ABCD, ABCDF, ABCDE, ABCDEF\}| = 24$$

 

What is missing?

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If you only consider Super keys which have A in them, then also that it 32. So, you have not even included super keys consisting of A.

Answer 2

Getting 44 by applying principle of inclusion exclusion method to the 3 groups of CKs(A,BC,CD)