Discussion
In a relational data model, which one of the following statements is TRUE?
Answer: A
The true statement is A relation with only two attributes is always in BCNF.
For a relation R(A, B), the only possible non-trivial dependencies are A → B and B → A. If A → B holds, A is a key; if B → A holds, B is a key; if neither holds, the key is AB and there is no non-trivial dependency to violate BCNF. In every case each determinant is a superkey.
The others are false. R(A, B, C) with AB → C and C → B has keys AB and AC, so every attribute is prime, yet C → B violates BCNF because C is not a superkey. A relation whose key is all of its attributes has no non-prime attribute at all. And BCNF decomposition can lose dependencies: decomposing that same relation into BCNF loses AB → C.
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