ABSTRACT
Remark 1.4.7 Theorem 1.4.6 is also satisfied for arbitrary families of congruence relations on A. But in general, the union of two congruence relations of an algebra A is not a congruence relation, since this does not hold even for equivalence relations, as the following example shows. Take
A = {1, 2, 3}, 01 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)1, 02 = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}.
