Projecting the fds stated over a set of attributes x onto a

Question

Let R be decomposed into R₁, R₂, ..., R_n. Let F be a set of FDs on R

1. Define 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.