For the following questions select your answer, providing a brief explanation of your answers. You will not

receive marks for answers without explanation.

a$.$ Consider a relation R$($A$,$B$,$C$,$D$,$E$)$ with functional dependencies: AB$->$C$,$ C$->$D$,$ BD$->$E$.$ Which of the following

sets of attributes does not functionally determine E$?$

$()$

$()$ ACD

$()$ AB

$()$ BE

b$.$ Consider a relation R with five attributes ABCDE. You are given the following dependencies: A $->$ B$,->$ E$,$

and ED $->$ A$.$ State the strongest normal form that the relation is in$.$

$()1$NF

$()2$NF

$()3$NF

$()$BCNF

c$.$ Consider a relation R$($A$,$B$,$C$,$D$,$E$)$ with functional dependencies: D$->$C$,$ CE$->$A$,$ D$->$A$,$ AE$->$D$.$ Which of the

following is a key?

$()$

$()$ AD

$()$ CDE

d$.$ Let relation R$($A$,$B$,$C$,$D$,$E$)$ satisfy the following functional dependencies: AB$->$C$,$ BC$->$D$,$ CD$->$E$,$ DE$->$A$,$ AE$->.$

Which of the following FDs is also guaranteed to be satisfied by R$?$

$()->$

$()$ AD $->$B

$()->$

$()$ A$->$C