select all the right options
$\forall_{t_1, \;t_2 \;\in \;r(R)}\big[(t_1(\alpha)=t_2(\alpha))\; \rightarrow (t_1(\beta)=t_2(\beta))\big]$ implies that there is $\alpha \rightarrow \beta$ functional dependency in relation $r$ with relation schema $R$, here $t_1$ and $t_2$ are the tuples in the instance $r$.
If $K$ is a superkey of a relation instance $r$ of a relation schema $R$ then $\forall_{t_1, \;t_2 \;\in \;r(R)}\big[(t_1(K)=t_2(K))\; \rightarrow (t_1(R)=t_2(R))\big]$. Here $t_1$ and $t_2$ are the tuples in the instance $r$.
A relational decomposition is said to be dependency preserving if enforcement of all functional dependencies should be possible on individual decomposed relations or when they joined.