GATE1988-12i

Question

What are the three axioms of functional dependency for the relational databases given by Armstrong.

Answer 1

1. AXIOM OF REFLEXIVITY

If $Y\subseteq X$ then   $X\rightarrow Y$

2. AXIOM OF AUGMENTATION

If   $X\rightarrow Y$ then   $XZ\rightarrow YZ$ for any Z

3. AXIOM OF TRANSITIVITY

If   $X\rightarrow Y$  and   $Y\rightarrow Z$  then   $X\rightarrow Z$

Comments

If  $Y\subseteq X$  then  $X\rightarrow Y$

$\implies \text{Axiom of reflexivity is also called a trivial functional dependency.}$