Sets And Relations

Let a set A = A₁ \(\cup\) A₂ \(\cup\) ..... \(\cup\) A_k, where A_i \(\cap\) A_j = \(\phi\) for i \(\ne\) j, 1 \(\le\) j, j \(\le\) 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 \(\le\) i \(\le\) k}. Then, R is :