How to normalise a relation using functional dependencies G = {{A,B}→{C},{B,D}→{E,F},{A,D}→{G,H},{A}→{I},{H}→{J} }.


Which is a key attribute: {A,B} or {A,B,D}?
A simple way to check if a set of attributes is a key, is to compute the closure of those attributes with respect to the functional dependencies, and see if this contains all the attributes of the relation.

So:

{A B}+ = {A B C I}

{A B D}+ = {A B C D E F G H I J}

And so {A B D} is a key. You can also see that every key must contain A B D since those attributes appear only in the left parts of the dependencies, and since {A B D} by themselves are a key, there are no other keys.