1.
Let a set A=A1∪A2∪⋯∪AkA = A_1 \cup A_2 \cup \dots \cup A_k, where Ai∩Aj=∅A_i \cap A_j = \varnothing for i≠ji \neq j; 1≤i,j≤k1 \le i, j \le k. Define the relation RR from AA to AA by R={(x,y):y∈Ai if and only if x∈Ai,1≤i≤k}R = \{(x, y): y \in A_i \text{ if and only if } x \in A_i, 1 \le i \le k\}. Then RR is: