Why are certain functional dependencies called trivial functional dependencies?

Explain what is meant by repetition of information and inability to represent information. Explain why each of these properties may indicate a bad relational database design.

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

{AB-> C, CD -> E, DE -> B} 

Is AB a candidate key of this relation? If not, is ABD? Explain your answer. 

No. The closure of AB does not give you all of the attributes of the relation.

If not, is ABD? Explain your answer. 

Consider a relation with schema R(A,B,C,D) and FDs {AB -> C, C -> D, D -> A}. 

a. What are some of the nontrivial FDs that can be inferred from the given FDs? 

Consider a relation R(A,B,C,D,E) with FDs {AB -> C, DE ->C, and B -> D} 

a. Indicate all BCNF violations for R.

Prove or disprove the following inference rules for functional dependencies. 

Note: Read "|=" as implies 

a. {X->Y, Z->W} |= XZ ->YW 

Consider a relation R(A,B,C,D) with FDs {A ->B, B ->C, C-> D} 

a. Indicate all BCNF violations for R. 

For the same example relation R with the two tuples as in the notes above, decompose it as R1(A,B) and R2(A,C). Try and merge them back using natural join and see if the resulting relation is the same as R. Do you think this decomposition is a lossless join decomposition?