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$)$ if aR$1$c and bR$2$d$.$ Is R a total order? If the answer is yes, please prove it; otherwise, give a counter example.