7.24

Why are certain functional dependencies called trivial functional dependencies?

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Let \(r(R)\) be any relation. Let \(\alpha \subseteq R, \beta \subseteq R, \text{ and } \beta \subseteq \alpha\). Then we know that the functional dependency \(\alpha \rightarrow \beta\) holds even though we don’t know any thing about \(r(R)\). \(r(R)\) could have been any relation and our statement will hold true. This is unintersting to us, so we call it trivial.