Let a set A = A_1 ∪ A_2 ∪ … ∪ A_k, where A_i ∩ A_j=φ for i ≠ j, 1 ≤ i, j ≤ k. Define the relation R from A to A by R ={(x, y): y ∈ A_i. if and only…

Let a set $\displaystyle \mathrm{A}=\mathrm{A}_1 \cup \mathrm{~A}_2 \cup \ldots \cup \mathrm{~A}_k$, where $\displaystyle \mathrm{A}_i \cap \mathrm{~A}_j=\phi$ for $\displaystyle i \neq j, 1 \leq i, j \leq k$. Define the relation R from A to A by $\displaystyle \mathrm{R}=\left\{(x, y): y \in \mathrm{~A}_i\right.$ if and only if $\displaystyle \left.x \in \mathrm{~A}_i, 1 \leq i \leq k\right\}$. Then, R is :