Consider the following relation R $($A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G$)$ where all attributes are

atomic. The following functional dependencies are identified:

$$ A$,$B $$ C

$$ C $$ E$,$ F

$$ A $$ E

$$ F $$ G

$1.$ Give the primary Key of R $(6$ points$)$

$2.$ Is R is the first normal form? Why or why not $(2$ points$)$

$3.$ Is R in the second normal form? Why or why not. If not, decompose into

relations that are in the second normal form. $(6$ points$)$

$4.$ Are the relation obtained in question$(3)$ in the third normal form? Why

or why not. If not decomposed into relations that are in the third normal

form $(6$ points$)$