For any string w $=$ w$1$w$2$ wn$,$ the reverse of w$,$ written wR$,$ is the string w in reverse order;

that is$,$ wR $=$ wn w$2$w$1.$ For any language A$,$ let AR $=$ fwR j w $2$ Ag$.$ Show that if A is

regular, so is AR$.$For any string $w=w_1{w}_{2}cdots{w}_n,$ the reverse of $w,$ written $w^R,$ is the string $w$ in reverse order;

that is$,w^R=w_{n}cdots{w}_2{w}_1.$ For any language $A,$ let $A^R=\{w^R|winA\}.$ Show that if $A$ is

regular, so is $A^R.(8$ points$)$