Suppose you are given a relation scheme R = {A, B, C, D}. For each of the following sets of functional dependencies, assuming those are the only dependencies that hold for R, do the following: i. Identify the candidate key(s) for R. ii. State whether or not the proposed decomposition of R into smaller relations is a good decomposition, briefly explaining why or why not. 1. {B -> C, D -> A}: decompose into BC and AD. 2. {AB -> C, C -> A, C -> D}: decompose into ACD and BC. 3. {A -> BC, C -> AD}: decompose into ABC and AD. 4. {A -> B, B -> C, C -> D}: decompose into AB and ACD. 5. {A -> B, B -> C, C -> D}: decompose into AB, AD and CD.