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I have a homework question that I am trying to understand but having a tough time with this question. Any explanation or even pointers would be very appreciated (no exact answer expected - I am trying to learn - but any help would be great).

I have two relations with a set of explicitly defined constraints.

D = {R1:CDE, R2:FGH}  Constraints = {R1: CD->E, R2:key(G), R1[DE] subset R2[FG]}

Are the two relations (D={R1 and R2}) in BCNF?

Thank you for any guidance you can provide.

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A relation is in BCNF if every determinant of the non-trivial dependencies is a superkey.

If G is the key of R2, we know that G → F and G → H.

Since DE in R1 is a subset of FG in R2, and since G → F, we can easily prove that E → D in R1.

If no other constraint holds on R1, then we can calculate the candidate keys of R1 starting from the two dependencies CD → E and E → D, and see if R1 is in BCNF or not.

Finally note that, if no other constraint is known on R2 a part from the key, it is very easy to decide if it in BCNF or not.

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