Functional dependencies

[pinion9]

It has been quite some time since I have done anything like this. It is for a database class and we are working with functional dependencies.

For Example:

? IR2, Augmentation Rule
X --> Y implies XZ --> YZ
? IR3, Transitive Rule
X --> Y, Y --> Z implies X --> Z
? IR5, Union, or Additive, Rule
X --> Y, X --> Z implies X --> YZ

My question is, can these types of rules work in reverse? E.g. for the Union rule, would it be correct to break a statement down

X --> YZ implies X --> Y, X --> Z

Or does it not work that way?

 

[TuxDave]

What does X -> YZ mean in terms of if then? I'm not a database person but if translated into if X then Y AND Z, then you can make the conclusion that if X then Y and if X then Z.

To be very general, I would say when things 'imply' another, it doesn't necessarily work in reverse. If you are a man, it implies that you're human. But if you're a human it doesn't imply that you're a man.