Let a set $A = A_{1} \cup A_{2} \cup \ldots.. \cup A_{k}$, where $A_{i} \cap A_{j} = \phi$ for $i \neq j,1 \leq i,j \leq k$. Define the relation $R$ from $A$ to $A$ by $R = \{(x,y):y \in A_{i}$ if and only if $x \in A_{i},1 \leq i \leq k\}$. Then $R$ is