Let A = {1,2,3,4, 5}. Let {1,2,3} and {4, 5} be two equivalence classes of a relation R on A. The number of elements in R is

R must contain 5 elements $(\mathrm{a},\mathrm{a})\mathrm{\forall }\mathrm{a}\in \mathrm{A}$

As {1, 2, 3} is an equivalence class, (1,2). (1, 3). (2, 3). (2, 1). (3, 1), (3, 2) $\in$ R

Next, as {4,5} is an equivalence class, (4, 5), (5, 4) $\in$ R. 

Thus, R contains 5 + 6+2 =13 elements.