Example for Augmentation rule in DBMS

Question

Augmentation rule in Functional dependencey states that

when X -> Y ,

then XZ->YZ.

Can some one give an real world example of this?

Answer 1

If X is customer ID and Y is customer name and Z is birth date, then :

X->Y means that if you are given a customer ID, it is possible to determine a customer name from that.

XZ->YZ means that if you are given both a customer ID and a birth date, then it is possible to derive customer name and birth date from that.

A UNION of "givens" is sufficient to determine the UNION of the results corresponding to [each of] those "givens".

And a thing being "given" is of course trivially sufficient to determine the thing. (That's the Z->Z part).