Let a set $A=A_1 \cup A_2 \cup \ldots \cup A_{k^{\prime}}$ where $A_i \cap A_j=\phi$ for $i \neq j 1 \leq i_{\text {n }} j \leq k$. Define the relation $R$ from $A$ to $A$ by $R= \left\{(x, y): y \in A_i\right.$ if and only if $\left.x \in A_i, 1 \leq i \leq k\right\}$. Then, $R$ is:
