1- Prove that any relation schema with two attributes is in BCNF.
2- R(A, B, C) is a relation in BCNF. A is one of the keys of R. R may have other keys.
Prove that R is in 4NF.
(Hint: Assume that R is not in 4NF. What could the MDs that violate 4NF be?
For each such MD, use what you know about the relation to show that this MD cannot violate 4NF.)
3- Consider the universal relation R = {A, B, C, D, E, F, G, H, I} and the set of functional dependencies
F = { {A, B} -> {C}, {A} -> {D, E}, {B} -> {F}, {F} ->{G, H}, {D} -> {I, J} }.
What is the key for R? Decompose R into 2NF, then 3NF relations.