How many equivalence relations can be defined on the set $S\{1,2,3,4\}$ such that the partition has exactly two equivalence classes, one of size 2 and the other of size 2?

Step-by-step solution

1. A partition with two blocks of size 2 is determined by choosing which two elements form the first block.
2. Number of ways to choose 2 elements out of 4: C(4,2)=6.
3. But swapping the two blocks does not give a new partition, so divide by 2.
4. Thus number of such partitions = 6/2 = 3.
5. Each partition corresponds to exactly one equivalence relation.

Concept tested: Counting equivalence relations via partitions

Published 1 October 2026 · How this solution was prepared and checked