Prove that any relation schema with two attributes is in BCNF.
What will be an ideal response?
Consider a relation schema R={A, B} with two attributes. The only possible (non-trivial)
FDs are {A} ->{B} and {B} ->{A}. There are four possible cases:
(i) No FD holds in R. In this case, the key is {A, B} and the relation satisfies BCNF.
(ii) Only {A} ->{B} holds. In this case, the key is {A} and the relation satisfies BCNF.
(iii) Only {B} ->{A} holds. In this case, the key is {B} and the relation satisfies BCNF.
(iv) Both {A} ->{B} and {B} ->{A} hold. In this case, there are two keys {A} and {B} and
the relation satisfies BCNF.
Hence, any relation with two attributes is in BCNF.
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