A\(\times A\) congruence coherent implies A congruence permutable (Q1096657)

The content of this one-page article is the proof of the assertion in the title. An algebra A is called congruence coherent, if every subalgebra of A containing one class of a congruence on A is a union of classes of that congruence. The product \(\rho\circ \sigma\) of two binary relations \(\rho\), \(\sigma\) on the same set is defined so that (a,b)\(\in \rho \circ \sigma\) if and only if there exists c such that (a,c)\(\in \rho\), (c,b)\(\in \sigma\). If \(\rho \circ \sigma =\sigma \circ \rho\) for any two congruences \(\rho\), \(\sigma\) on an algebra A, then A is called congruence permutable.