Functional Dependecies

if ${\pi }_X(t1)={\pi }_X(t2)$ then ${\pi }_Y(t1)={\pi }_Y(t2)$

“if two tuples agree on their X-values, then they also agree on their Y-values”

trivial

$X\to Y$ is trivial if $Y\subset X$.

completely non-trivial

$X\to Y$ is completely non trivial if $Y\cap X=\varnothing$.

multible right hand side attributes

A_{1}... A_{n} \rightarrow B_{1} ... B_{m} \Rightarrow \begin{array}{ccc} A_{1}... A_{n} & \rightarrow & B_{1} \\ \vdots & & \vdots \\ A_{1}... A_{n} & \rightarrow & B_{m} \\ \end{array}$$