Definition:(2-3) Parastrophe

Definition
Let $\left({S, \circ_1}\right)$ and $\left({S, \circ_2}\right)$ be magmas.

Then $\left({S, \circ_2}\right)$ is a $(2-3)$parastrophe of $\left({S, \circ_1}\right)$ iff:


 * $\forall x_1, x_2, x_3 \in S: x_1 \circ_1 x_2 = x_3 \iff x_1 \circ_2 x_3 = x_2$