Discussion
Armstrong (1974) proposed systematic approach to derive functional dependencies. Match the following w.r.t. functional dependencies :
| List - I | List - II |
|---|---|
| a. Decomposition rule | i. If \(X \to Y\) and \(Z \to W\) then \(\{X, Z\} \to \{Y, W\}\) |
| b. Union rule | ii. If \(X \to Y\) and \(\{Y, W\} \to Z\) then \(\{X, W\} \to Z\) |
| c. Composition rule | iii. If \(X \to Y\) and \(X \to Z\) then \(X \to \{Y, Z\}\) |
| d. Pseudo transitivity rule | iv. If \(X \to \{Y, Z\}\) then \(X \to Y\) and \(X \to Z\) |
Codes : a b c d
Answer: D
The match is a-iv, b-iii, c-i, d-ii. The decomposition rule says that if X determines {Y, Z} then X determines Y and X determines Z (iv). The union rule says that if X determines Y and X determines Z then X determines {Y, Z} (iii). The composition rule joins two dependencies, X to Y and Z to W giving {X, Z} to {Y, W} (i). Pseudo transitivity says that if X determines Y and {Y, W} determines Z then {X, W} determines Z (ii).
The other codes confuse union with decomposition, since they run in opposite directions.
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