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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?

1. {E, F}
2. {E, F, H}
3. {E, F, H, K, L}
4. {E}

Correct answer: {E, F, H}

Solution

The correct option {E, F, H} is a key for relation R because it can determine all other attributes in the relation through the given functional dependencies. Specifically, {E, F} can derive {G, I, J}, and adding {H} allows us to derive {K, L}, which in turn can derive {M} and {N}, thus covering all attributes.

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