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 $\alpha \to \beta$ 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.