Let R be decomposed into R1, R2, ..., Rn. Let F be a set of FDs on R.
1. De?ne what it means for F to be preserved in the set of decomposed relations.
2. Describe a polynomial-time algorithm to test dependency-preservation.
3. Projecting the FDs stated over a set of attributes X onto a subset of attributes Y requires that we consider the closure of the FDs. Give an example where considering the closure is important in testing dependency-preservation, that is, considering just the given FDs gives incorrect results.