Is there any common application for the union of two cartesian products on two sets? Given two sets, $A$ and $B$, is there any common application of $({A\times B})\cup(B\times A)$? The two orderings only ever contain similar elements if $A\cap B \neq\emptyset$, so I imagine combing the two could yield something.

Viewed as a relation for A $\cup$ B,
(A×B) $\cup$ (BxA) is the symmetric closure of A×B.