How many equivalence relations are there on $\{1, 2, 3, 4\}$?

Explanation

1. 01

   Count the splits of 4 elements: one class (1), 3 + 1 (4), 2 + 2 (3), 2 + 1 + 1 (6), four singles (1).

2. 02

   $1 + 4 + 3 + 6 + 1 = 15$.