Q: On {1,2,3}, R = {(1,1),(2,2),(3,3),(1,2),(2,1)}. Check reflexive, symmetric, transitive. Reflexive: yes (all (a,a) present). Symmetric: yes ((1,2)↔(2,1)). Transitive: yes (check (1,2),(2,1)→(1,1) present). So R is an equivalence relation.