Functional dependency

Question

        if  x->a  and y-> b 
        then 
        from  x->a  ==   xy-->ay   [ir2]   xy-->a [ir4]
        from  y->b  ==   xy-->xb   [ir2]   xy-->b [ir4] 
        therefore xy-->ab  [ir5]

But elmasri navathe says , x-->a and y-->b DOES NOT IMPLY xy-->ab i am just starting with functional dependency , so could some one point out what i am missing ?

Answer 1

I just checked C J DATE , where in chapter 11 , page 339 it lists a rule called composition , if a->b , c->d then ac->bd , so that answers part of my query but am curious as to why it says otherwise in navathe .