Let $($A$,$ R$1)$ and $($B$,$ R$2)$ be two total orders, where A $=\{1,2,3\},$ B $=\{$x$,$y$,$z$\}.$ Define R on A x B by $($a$,$b$)$R$($c$,$d$).$ Is R a total order? If the answer is yes, please prove it; otherwise, give a counter example.