Consider a set of boolean variables $\{$x $+1,...,$ xn$\}$ and the $2^$n possible assignments of truth values to these variables. If f and g are two such assignments, define f $+$ g to be the assignment h where h$($xi$)=$ f $($xi$)$ g$($xi$),$ and define f g similarly in terms of $.$ Prove that these two operators obey the semiring axioms.