Consider a relation scheme R = (A, B, C, D, E, H) on which the following…
2005
Consider a relation scheme R = (A, B, C, D, E, H) on which the following functional dependencies hold: {A → B, BC → D, E → C, D → A}. What are the candidate keys of R?
- A.
AE, BE
- B.
AE, BE, DE
- C.
AEH, BEH, BCH
- D.
AEH, BEH, DEH
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Correct answer: D
Step 1: Identify attributes that do not appear on the right-hand side of any functional dependency. These must be part of every candidate key. In this relation, E and H do not appear on the right-hand side.
Step 2: Compute the closure of {E, H}. Using E → C gives us {C, E, H}. We still need A, B, and D.
Step 3: Add attributes to {E, H} to form candidate keys. Testing {A, E, H}: A → B and E → C allows us to derive D via BC → D. Closure is {A, B, C, D, E, H}. Testing {B, E, H}: E → C allows BC → D and D → A. Closure is {A, B, C, D, E, H}. Testing {D, E, H}: D → A and A → B allows us to get C via E. Closure is {A, B, C, D, E, H}.
Step 4: The candidate keys are AEH, BEH, and DEH.
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