multivalued dependency

a multivalued dependency $\text{[math]}$ specified on relation schema $\text{[math]}$ , where $\text{[math]}$ and $\text{[math]}$ are both subsets of $\text{[math]}$ , specifies the following constraint on any relation state $\text{[math]}$ of $\text{[math]}$ : if two tuples $\text{[math]}$ and $\text{[math]}$ exist in $\text{[math]}$ such that $\text{[math]}$ , then two tuples $\text{[math]}$ and $\text{[math]}$ should also exist in $\text{[math]}$ with the following properties, where we use $\text{[math]}$ to denote $\text{[math]}$ :

$\text{[math]}$
$\text{[math]}$ and $\text{[math]}$ $\text{[math]}$ and $\text{[math]}$

wherever $\text{[math]}$ holds, we say that $\text{[math]}$ mmultidetermines $\text{[math]}$ . because of the symmetry in the definition, whenever $\text{[math]}$ holds in $\text{[math]}$ , so does $\text{[math]}$ . hence, $\text{[math]}$ implies $\text{[math]}$ and therefore is sometimes written as $\text{[math]}$ .
[cite:;from @elmasri_db_2015 chapter 14.6.1 formal definition of multivalued dependency]