Slide 16.7: A minimum set of functional dependencies Slide 16.9: Closure and cover (cont.) Home

Closure and Cover

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Closure of a Set of Functional Dependencies
Given a set F of FDs on attributes of a table T, the closure of F, symbolized by F+, to be the set of all FDs implied by F.

Note: The set of FDs that is implied by a set of F of FDs could grow exponentially.

FD Set Cover
FD set cover is introduced and is used to find a minimal set.

• A set F of FDs on a table T is said to cover another set G of FDs on T, if G⊆F+.


• If F covers G and G covers F, then F≡G.

A Question of FD Set Cover Demonstrate that F covers G.

F = { B→CD, AD→E, B→A }   G = { B→CDE, B→ABC, AD→E }

Answer
Take the following steps to show F covers G:

1. By Union Rule, B→CD and B→A ⇒ B→ACD.


2. By Union Rule, B→B and B→ACD ⇒ B→ABCD.


3. By Decomposition Rule, B→ABCD ⇒ B→AD.


4. By Transitivity Rule, B→AD and AD→E ⇒ B→E.


5. By Union Rule, B→ABCD and B→E ⇒ B→ABCDE.


6. By Decomposition Rule, B→ABCDE ⇒ B→CDE and B→ABC.

Slide 16.7: A minimum set of functional dependencies Slide 16.9: Closure and cover (cont.) Home

Jennifer’s presentation was on point (well done) —           concise, relevant, and accurate.