# Composition for Functional Depedencies

Suppose I have the following Functional Dependencies for a Relational Model:

$A \to C$

$B \to C$

According to the composition rule for functional dependencies we have:

If X → Y and Z → W, then XZ → YW


For the case above would it be correct to say:

$AB \to CC$

$AB \to C$

Would the composite $CC$ be the same as just $C$? And for a relational model would it be proper to separate $C$ into a relation such that $AB$ is the Primary Key? Or should I simply drop either of the relations $A \to C$ or $B \to C$?

I was told by my database professor that $AB \to C$ is wrong and I should dropped one of them when I have created a Logical Data Model. But I don't understand how what I said above is wrong.