Let $S = \left\{ S_1,S_2,\dots S_n \right\}$ be a finite collection of finite sets. A system of distinct representatives, or SDR, of $S$ is a set $$x_1 \in S_1, x_2 \in S_2, \dots x_n \in S_n$$ such that $$x_i \neq x_j \text{ whenever } i \neq j$$ (i.e., each choice must be unique).