Consider a relation with schema RA B C D and FDs AB rightarr

Consider a relation with schema R(A, B, C, D) and FD\'s: AB rightarrow C, C rightarrow D, and D rightarrow A. Report any five nontrivial FD\'s that can be derived from the given FD\'s. Use the properties like Transitivity, and Augmentation. Find the attribute closure for the following attribute sets: {AD}, {C}, {AB} What are all the candidate keys of R?

Solution

1) C -> A ( by transitivity)

AB -> D ( by transitivity)

AB -> A( by transitivity)

BD -> C ( by trans and aug)(BD->AB, AB-> C)

BD -> D

2) {AD}= { A.D}

{C}= {C,D,A}

{AB} = {A,B,C,D,}

3) AB is the candidate key. Because closure of AB cover all the attributes.

AB , BD,BC