(Solved): Consider the universal relation R = {A, B, C, D, E, F, G, H} and the set of functional dependen ...

a) Consider the universal relation \( R=\{A, B, C, D, E, F, G, H\} \) and the set of functional dependencies \( \exists=\{\{A, B\} \rightarrow\{C\},\{B\} \rightarrow\{D\},\{E\} \rightarrow\{F, G\},\{D\} \rightarrow\{H\}\} \). 1) What is the key for \( R \) ? 2) If \( R \) is not in \( 2 N F \), first decompose it into \( 2 N F \) and then 3NF relations; if \( R \) is in \( 2 N F \) but not in \( 3 N F \), decompose it into 3 NF relations; otherwise, do nothing. b) Design a proper DTD for the FitnessCenter XML document. c) For the following queries on the XML document below for classes, write the corresponding XPath expressions. 1) Find the work phone number of Roger. 2) Find the name of all members at the platinum level. 3) When pointing to the level attribute of "Jeff", find the level attribute of the member next to "Jeff". \( < \) ?xml version="1.0"?> \( < \) FitnessCenter> \( \langle \) Member id=" 1 " level=" gold"> \( < \) Name \( > \) Jeff \) \( < \) Phone type="home">555-1234 \) \( < \) Phone type \( = \) "work" \( >555-4321 \) \( < \) FavoriteColor>lightgrey \( < \) /Member> \( < \) Member id="2" level="gold"> \( < \) Name \( > \) David \) \( < \) Phone type="home">383-1234 \( < \) Phone type="work" \( >383-4321 \) \( < \) FavoriteColor>lightblue \( \( \langle \) Member id="3" level="platinum"> \( < \) Name \( > \) Roger \( \) \( < \) Phone type="home">888-1234 \( < \) Phone type="work"> \( 888-4321 \) \( < \) FavoriteColor>lightyellow \( < \)