Q1 Consider a relation schema r(A,B,C,D,E, F) and a set of functional dependencies {A BCD,BCDE,BD,DA}

1) Compute a canonical cover for the above set of functional dependencies (show each step of your derivation with an explanation).

2)Compute the closure of AF and then determine whether or not AF is a candidate key.

3) Suppose that (A,B, F) is decomposed into (A, F) and (B, F). Given the above functional dependencies, is this decomposition always lossless? If so, prove this. Otherwise, explain it using an example.

4) Determine whether or not (A,E, F) is in BCNF and justify your answer. If (A,E, F) is not in BCNF,find a BCNF decomposition of it

Q2 functional dependencies α->β and γ-> β do not imply α->γ prove this using an example relation.