 # Question & Answer: Given R(A, B, C, D, E, } with function dependencies {A rightarrow B, BC rightarrow DA, BD rightarrow C, E rightarrow A….. Given R(A, B, C, D, E, } with function dependencies {A rightarrow B, BC rightarrow DA, BD rightarrow C, E rightarrow A, AC rightarrow DE} a) Find all candidate keys. (Number each candidate key for credit and show your work for credit) b) What attributes of F are prime?

Given R(A,B,C,D,E)

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Question & Answer: Given R(A, B, C, D, E, } with function dependencies {A rightarrow B, BC rightarrow DA, BD rightarrow C, E rightarrow A…..
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We have following superkeys

1. ABCDE (All atributes is always a super key)
2. ACDE (As A->B)
3. BCE   (As BC->DA)
4. ABDE (As BD->C)
5. BCDE (As E->A)
6. BAC   (As AC->DE)

So in the above list the minimal set superkeys are BCE & BAC. All other can be trimmed down. So candidate keys are BCE & BAC.

b) Prime attributes are the attributes in the candidate keys so the prime attributes are B,C,E and A