# Are these relations in BCNF?

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.

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.