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Consider a relation R(A,B,C,D,E) with the following functional dependencies.

A→BC

C→E

B→D

E→A

The total number of super keys present in the relation are_______

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A, C and E are candidate key.

Using the principle of Inclusion-Exclusion we can find the number of the candidate key.

$n(A) + n(C) + n(E) - n(A \bigcap C) + n(A \bigcap E) + n(C \bigcap E) + n(A \bigcap C \bigcap E)$

$=>  2 ^{4} + 2 ^{4} + 2 ^{4} - 2 ^{3} - 2 ^{3} - 2 ^{3} + 2 ^{2} = 28$
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=  S.K(A) + S.K(C) + S.K(E) - S.K(A $\bigcap$  C) - S.K (C $\bigcap$ E) - S.K(A $\bigcap$ E) + S.K(A $\bigcap$ C $\bigcap$ E)

= 24 + 24 + 24  - 23 -23-23 + 22

= 28

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