Inference rules for functional dependencies, X->A, Y->B, XY->AB

Question

As it says in the title I have trouble understanding why if we have X->A and Y->B then why is it wrong to write XY->AB. They way I understand it, if A is functionally dependent of X and B is functionally dependent of Y, then when we have XY on the left side we should have their corresponding values on the right side. Anyway my book says that this is wrong, so can anyone give me an example where this is proven wrong ? Thanks in advance :)

Answer 1

You're going about this the wrong way.

In order for "{X->A, Y->B}, therefore XY->AB" to be true, you need to prove that you can derive XY->AB from {X->A, Y->B}, using only Armstrong's axioms and the additional rules derived from Armstrong's axioms.

Answer 2

If X uniquely determines A and similarly Y uniquely determines B ,then any combination of XY uniquely determines AB.

Hence , X->A ,Y->B infers XY->AB is true.

More supporting links.

http://en.wikipedia.org/wiki/Functional_dependency…

See the composition rule here. Not crebile enough ? Then in the following link , Slide 9 says that

Textbook, page 341: ”… X A, and Y B does not imply that XY AB.” Prove that this statement is wrong.

http://www.ida.liu.se/~TDDD37/fo/fo-normalization

Moreover, Mike's answer is trying to prove the "vice versa" , which may not necessarily be true.