Problem $1.$ Consider a relation R$($A$,$ B$,$ C$,$ D$,$ E$)$ with the following dependencies: AB $$ C$,$ CD $$ E$,$ DE $$ B Is AB a candidate key of this relation? If not, is ABD? Explain your answer. Problem $2.$ Consider the following relation: CAR$\_$SALE$($Car#$,$ Date$\_$sold, Salesperson#$,$ Commission$\%,$ Discount$\_$amt$)$ Assume that a car may be sold by multiple salespeople, and hence $\{$Car#$,$ Salesperson#$\}$ is the primary key. Additional dependencies are Date$\_$sold $$ Discount$\_$amt and Salesperson# $$ Commission$\%$ Based on the given primary key, is this relation in $1$NF$,2$NF$,$ or $3$NF$?$ Why or why not? How would you successively normalize it completely? Problem $3.$ Consider the following relation for published books: BOOK $($Book$\_$title, Author$\_$name, Book$\_$type, List$\_$price, Author$\_$affil, Publisher$)$ Author$\_$affil refers to the affiliation of author. Suppose the following dependencies exist: Book$\_$title $$ Publisher, Book$\_$type Book$\_$type $$ List$\_$price Author$\_$name $$ Author$\_$affil a$.$ What normal form is the relation in$?$ Explain your answer. b$.$ Apply normalization until you cannot decompose the relations further. State the reasons behind each decomposition.