Let a set $A = A_1 \cup A_2 \cup \cdots \cup A_k$, where $A_i \cap A_j = \phi$ for $i \ne j$, $1 \le i, j \le k$. Define the relation $R$ from $A$ to $A$ by $R = {(x,y) : y \in A_i \text{ if and only if } x \in A_i, ; 1 \le i \le k}$. Then, $R$ is :