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

8. Obvious
9. $R(A,B,C,D,E,G)$ decomposes into $R_{1}(A,B,C)$, $R_{2}(A,C,D,E)$, $R_{3}(A,D,G)$ The FDs $B\rightarrow D$, $E\rightarrow G$ are not preserved.
   $R_{1}$ and $R_{2}$ are decomposed losslessly because $AC\rightarrow B$
   $R_{2}$ and $R_{3}$ are decomposed losslessly because $AD\rightarrow E$ and $E\rightarrow G$ translates into $AD\rightarrow G$
10. #6 redone
11. 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)