$(15$ points$)$ You are given the following set of functional dependencies for a table with $7$

attributes $($ABCDEFG$)$:

A$$B$,$ A$$C$,$ CD$$G$,$ EG$$F$,$ AFG$$E

a$.$ Find all candidate keys $($show your work$)$

b$.$ Find a lossless decomposition into Boyce$-$Codd normal form with the following

instructions:

i$.$ If there is a choice of functional dependencies that can be used, pick the

leftmost one $($as listed on the question$)$ that has not been use.

ii$.$ If you have to replace a functional dependency with another, put the new one$($s$)$

at the end of the list.