Let R1 and R2 be two equivalence relations on the same set A

Let R1 and R2 be two equivalence relations on the same set A.

Express neatly the minimum requirement on R1 and R2 to make certain that their union will also be an equivalence relation.

Solution

minimum requirement for union to be an equivalence relation:

union should be reflexive relation

union should be symmetric relation

union should be transitive relation