Consider the following relational schema and set of functional dependencies. R$($A$,$B$,$C$,$D$,$E$)$ with functional dependencies AB$->$E and D$->$C$.$

a$.$ List all super key$($s$)$ for this relation. Which of these super keys form a key $($ie$,$ a minimal super key$)$ for this relation? Justify your answer in terms of functional dependencies and closures.

b$.$ Decompose R into BCNF$.$ Show your work for partial credit. Your answer should consist of a list of table names and attributes and an indication of the keys in each table $($underlined attributes$).$