Solve these without using AI tools or copy paste: $4.$ Prove that every NFA can be converted to an equivalent one that has a single accept state.

$($Give a constructive proof.$)$

$5.$ For any string w $=$ w$1$w$2...$wn$,$ the reverse of w$,$ written wR$,$ is the string w in reverse order, wn$...$w$2$w$1.$ For any language A$,$ let AR $=\{$wR $|$ w in A$\}.$ Show that if A is regular, so is AR$.$

$($Give a constructive proof. You need your solution to Exercise $4$ for this.$)$