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Functional dependencies

My question is related to functional dependencies. I would like to know an example of a relation for which the following result is not true:
a --> b and c --> b implies a --> c.

This is one of the more interesting pieces of functional decomposition to learn to understand. I'll use simple mathematics for an example.

If we start with the following assertions (functions):

A: 1 = n modulo 2
B: n is an integer
C: 0 = n modulo 2

The only class of numbers that satisfy A is odd integers. The only class of numbers that satisfies C is even integers. Any n that satisfies A implicitly satisfies B. Any n that satisfies C implicitly satisfies B. No n that satisfies A will ever satisfy C.

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