Closure and Cover (Cont.)

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 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.



      “The journey of a thousand miles begins with one step.”    
      — Lao Tzu