Prove that the following relation is an order on the Cartesian product {${1,2,3}$} × {${1,2,3}$} and draw its diagram.
$((x_1,x_2),(y_1,y_2))$ER if and only if $x_1 < x_2$ or $x_1=x_2$ and $y_1 ≤ y_2$
I can prove that this is reflexive, but I don't know how to prove it for anti-symmetricity and transivity.