Let a set \( A = A_1 \cup A_2 \cup \ldots \cup A_k \), where \( A_i \cap A_j = \phi \) for \( i \neq j \), \( 1 \le i, j \le k \). 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:
