The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.

Explanation

Let `R1 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}` and `R2 = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}` are two equivalence relations on set `A = {1, 2, 3}.`



Now, `R1 uu R2 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1)}. `



Since, `(2, 1) in R1 uu R2` and `(1, 3) in R1 uu R2`.



But `(2, 3) !in R1 uu R2`.



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