If I use the product construction to create a machine that recognizes L$($A$)\backslash$cup L$($B$)$ based on DFAs A $=($Q$\_$A$,\backslash$Sigma $,\backslash$delta $\_$A$,$ q$\_0$A$,$ F$\_$A$)$ and B $=($Q$\_$B$,\backslash$Sigma $,\backslash$delta $\_$B$,$ q$\_0$B$,$ F$\_$B$),$ how many states will the new machine have?