Data Management in Bioinformatics/Exercise 1

Figures are here: http://pipe.cs.vt.edu/~pbutler/bi_and_db/ until I can upload them (takes 4 days to get confirmed for media upload).

1. File:Problem1.svg
   Notes: 1) For each reservation, 1 <= # of drivers <= 10
2. 
   Notes:
   • A book seller must have at least one store.
   • A book store must be either web-based or brick, but not both.
3. Maximum: n is the case where all n are one-to-one. Minimum: n-1 is the case where n-1 one-to-many
4. File:Problem4.svg
5. File:Problem5.svg

6. FD Trivial $A \rightarrow B$ YES $B \rightarrow A$ NO $A \rightarrow C$ NO $C \rightarrow A$ NO $B \rightarrow C$ NO $C \rightarrow B$ YES

   MD Trivial $A \rightarrow \rightarrow B | A \rightarrow \rightarrow C$ YES $B \rightarrow \rightarrow A | B \rightarrow \rightarrow C$ NO $C\rightarrow \rightarrow A | C \rightarrow \rightarrow B$ YES

7. Obvious
8. R(A,B,C,D,E,G) decomposes into R₁(A,B,C), R₂(A,C,D,E), R₃(A,D,G)
   The FDs $B \rightarrow D$, $E \rightarrow G$ are not preserved.
   R₁ and R₂ are decomposed losslessly because $A C \rightarrow B$
   R₂ and R₃ are decomposed losslessly because $A D \rightarrow E$ and $E \rightarrow G$ translates into $A D \rightarrow G$
9. #6 redone
10. There are several solutions to this:

    LHS	RHS
    $B \cap C \rightarrow$	A − C	B − C	B (superset)
    $B \cap C \rightarrow$	A − B	C − B	C (superset)