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Chapter 10: Problem 10

When are two sets of functional dependencies equivalent? How can we determine their equivalence?

Short Answer

Expert verified
Two sets of functional dependencies are equivalent when they have the same closure. To determine their equivalence, we check that the closure of each set is a subset of the other set.

Step by step solution

01

Definition of Equivalent Functional Dependencies

Two sets of functional dependencies are equivalent if they have the same closure. In other words, the set of all dependencies that can be inferred from each set is the same.
02

Checking for Equivalence

To determine the equivalence of two sets of functional dependencies (let's call them \(X\) and \(Y\), both conditions \(X \subseteq Y^{+}\) and \(Y \subseteq X^{+}\) must hold true. Here, (\(+\)) represents closure, so \(Y^{+}\) denotes the closure of \(Y\), i.e., all dependencies that can be inferred from the set \(Y\). Similarly, \(X^{+}\) denotes the closure of \(X\). If both these conditions are met, we can say sets \(X\) and \(Y\) of functional dependencies are equivalent.

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Most popular questions from this chapter

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