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

A->BC

C->E

B->D

E->A

Total number of super key present in the relation are ______________.

Given answer is 28.

Please explain how?
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candidate keys for above relations are - A,C,E

Super key is a superset of candidate key. now considering each candidate calculate super key

no of super keys wih A(B,C,D,E)= $2^4$ (every attribute has 2 choices either i can be in superset or not)

no of super keys wih C(A,B,D,E)= $2^4$

no of super keys wih E(A,B,C,D)= $2^4$

no of super keys wih {A and C}(B,D,E)= $2^3$

no of super keys wih {C ad E}(A,B,D)= $2^3$

no of super keys wih {A and E}(B,C,D)= $2^3$

no of super keys wih {A and C and E}(B,D)= $2^2$

total number of superkeys = no of superkey (A U C U E)

= $2^4$ +  $2^4$ + $2^4$ - $2^3$ - $2^3$ - $2^3$ + $2^2$

= 28

 

please correct me if i'm wrong
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