Prove Theorem $2.$ i$.($x$,$y$+$z$)=($x$,$ y$)+($x$,$ z$)$ for all x$,$y$,$z ER$?.$ ii$.($x$,$cy$)=$ c$($x$,$ y$)$ for all x$,$y e R$2$ and all ceR. $($x$,$y$)=($y$,$ x$)$ for all x$,$ y ER$?$ If $($x$,$y$)=0$ for all x ERP, then y must be the zero vector. iv$.$