I have this relation:

R(A,B,C,D,E,G)
F = { AB -> C
AC -> D
AD -> E
B -> D
BC -> A
E -> G }

I need to project the original relation's functional dependencies onto the decomposed relations below. My question is, can I say that R3 carries E->G even though E->G is a deducted functional dependency based on a rule carried by R2? (AD->E)
And if so, is it correct to say that the key for R3 is A, D?

Or that.... no original FDs can pe projected onto R3 (since AD->E is not in THIS relation) and the key is ADG?


R1 (A, B, C) --- AB ->C, BC -> A
R2 (A, C, D, E) --- AC ->D, AD ->E
R3 (A, D, G) – AD->E (given) so E->G (transitive rule)