GATE CSE 1988 | Question: 12iib

Question

Using Armstrong’s axioms of functional dependency derive the following rules:

$\{ x \rightarrow y, \: wy \rightarrow z \} \mid= xw \rightarrow z$

(Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).

Answer 1

$x \rightarrow y$ (Given)

$\implies xw \rightarrow yw$ ( using axiom of augmentation $A \rightarrow B$ $\implies AX \rightarrow BX$)

also $yw \rightarrow z$ (Given)

$\implies xw \rightarrow z$ (using Axiom of transitivity ($A \rightarrow B$ and $B \rightarrow C)$ $\implies A \rightarrow C$)

Comments

This is psuedo transitivity !