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 $A\to B$ YES $B\to A$ NO $A\to C$ NO $C\to A$ NO $B\to C$ NO $C\to B$ YES

   MD Trivial $A\to \to B|A\to \to C$ YES $B\to \to A|B\to \to C$ NO $C\to \to A|C\to \to B$ 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 $B\to D$, $E\to G$ are not preserved.
   $R_1$ and $R_2$ are decomposed losslessly because $AC\to B$
   $R_2$ and $R_3$ are decomposed losslessly because $AD\to E$ and $E\to G$ translates into $AD\to G$
10. #6 redone
11. There are several solutions to this:

    LHS	RHS
    $B\cap C\to$	$A-C$	$B-C$	$B$ (superset)
    $B\cap C\to$	$A-B$	$C-B$	$C$ (superset)