7.2

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

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The nontrivial functional dependencies are \(A \rightarrow B\) and \(C \rightarrow B\), and a dependency they logically imply: \(AC \rightarrow B\). \(C\) 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 \(\alpha \rightarrow \beta\), where \(\beta \subseteq \alpha\).