Functional Dependencies and Keys. Consider the following relation and the data within it to answer the following parts of the question. Recall, any attribute can determine itself trivially, e$.$g$.$ A$->$ A$,$ B$->$B$,$ C$->$C$,$ D$->$D$.$ Also, any composition of attributes can determine its composed attributes; i$.$e$.$ AB$->$AB and AB$->$A and AB$->$B trivially. Include the trivial dependencies as well.

$\backslash$table$[[$A$,$B$,$C$,$D$],[$a$1,$b$1,$c$1,$d$1],[$a$1,$b$2,$c$2,$d$1],[$a$1,$b$3,$c$3,$d$2],[$a$2,$b$4,$c$4,$d$2],[$a$2,$b$4,$c$5,$d$3],[$a$3,$b$5,$c$6,$d$3]]$

a$.$ Which of the following can A determine? AB$,$ AC$,$ AD $?$

b$.$ Which of the following can B determine? BA$,$ BC$,$ BD $?$

c$.$ Which of the following can C determine? CA$,$ CB$,$ CD $?$

d$.$ Which of the following can D determine? DA$,$ DB$,$ DC $?$

e$.$ What can AB determine?

f$.$ What can AC determine?

g$.$ What can AD determine?

h$.$ What can BC determine?

i$.$ What can BD determine?

j$.$ What can CA determine?

k$.$ What are the super key$($s$)?$

l$.$ What are the candidate key$($s$)?$

m$.$ How many primary keys can a table have?