From below link on Functional Dependencies under FD Axioms(Armstrong's)
Reference Link on research
I came to know that ab→ c does NOT imply a → c and b → c
But, when I was reading the book "An Introduction to Database Systems" by C.J.Date, on page 279, there is an example that tells about reduction of following set of FDs:
A -> BC
B -> C
A -> B
AB -> C
AC -> D
and under point number 3 of the reduction process it further mentions: Next, we observe that the FD AB -> C can be eliminated, because again we have A -> C, so AB -> CB by augmentation, so AB -> C by decomposition.
So, that means that if A -> C, then we can imply AB -> C.
Assuming we are given the FD AB -> C in a separate case, then let us assume that A -> C, so AB -> C by above deduction, thus our assumption is true. Then, it proves the data in above link false! Is this mathematical approach not correct or I am wrong in a different way? Please throw some light on each perspective!