$[15$pts$]$ Consider a table instance with schema R$($A$,$B$,$C$,$D$,$E$)$ as below:

$(1)$ Which of the following dependencies can you infer that does not hold over schema R$.$ Justify your

answer for each FD using data from the given instance.

$($a$)$ A$->$C; $($b$)$ CD$->$A; $($c$)$ ABD$->$E

$(2)$ Find all the non$-$trivial functional dependencies that does hold on the given instance and only one

attribute on the left hand side.