Discussion
Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, N} and the set of functional; dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N}} on R. What is the key for R ?
Answer: B
The key is {E, F, H}.
E, F and H never appear on the right-hand side of any dependency, so every key must contain them. Their closure is the whole relation:
- {E, F} → G, and F → I, J;
- {E, H} → K, L;
- K → M and L → N.
So {E, F, H} determines all ten attributes and is minimal. {E, F} and {E} miss H, K, L, M and N. {E, F, H, K, L} is a superkey but not minimal, because K and L follow from E and H.
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