Functional Dependencies and Normalization $(20$ Points$)$

Consider the following relation R$($A$,$B$,$C$,$G$,$H$,$I$)$ and functional dependencies F that hold over R$.$

F $=\{$A $->$ B

A $->$ C

C$,$G $->$ H

C$,$G $->$ I

B $->$ H$\}$

Question $1\mathrm{.}7(4$ Points$).$ Determine all candidate keys of R$.$

Question $1\mathrm{.}8(6$ Points$).$ Compute the canonical cover of F$.$

Question $1\mathrm{.}9(4$ Points$).$ Determine in which normal forms relation R is$?$ Provide justification for your answer.

Question $1\mathrm{.}10(6$ Points$).$ Apply the $3$NF decomposition algorithm to relation R$.$