7.2

List all nontrivial functional dependencies satisfied by the relation of Figure 7.17.

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The nontrivial functional dependencies are $A\to B$ and $C\to B$, and a dependency they logically imply: $AC\to B$. $C$ does not functionally determine $A$ because the first and third tuples have the same $C$ value but different $A$ values. The same tuples also show $B$ does not functionally determine $A$. Likewise, $A$ does not functionally determine $C$ because the first two tuples have the same $A$ value and different $C$ values. The same tuples also show $B$ does not functionally determine $C$. There are 19 trivial functional dependencies of the form $\alpha \to \beta$, where $\beta \subseteq \alpha$.