candidate keys from functional dependencies

Question

Given the Relation R with attributes ABCDE. You are given the following dependencies: A -> B, BC -> E, and ED -> A. I already have the answer which is CDE, ACD, and BCD. I j

Answer 1

Use an algorithm;

1.Take any attribute or set of attributes

eg: ACD

2.Take the first mentioned functional dependency

eg: A -> B

3.Is the L.H.S of the dependency a subset of the attribute/s you chose in step 1?

If yes add the R.H.S of the functional dependency to the attribute. If no,ignore this functional dependency.

eg: A is a subset of ACD. So add B to ACD. ACD is now ABCD

4.Now go to the next functional dependency.Repeat step 3.

eg: BC -> E BC is a subset of ABCD. So ABCD is now ABCDE

5.If you have all the attributes now, you can stop.

If you don't have all the attributes, keep going to the next functional dependency and repeat step 3. If you have reached the last functional dependency and do not have all attributes, go back to the first functional dependency and repeat steps 3 and 4. Keep cycling in this loop until the set of attributes you have don't change no matter the functional dependency you repeat step 3 with.

eg: As I have ABCDE for attribute set ACD, I can stop.

If you have all attributes you have a superkey. eg: ACD is a superkey because I have ABCDE.