Q $3.(15$ points$)$ For two equal$-$length binary strings $w_1$ and $w_2,$ let $w_{1}o+w_2$ denote their bit$-$wise

XOR. Define the XOR of two languages A and $B$ over the binary alphabet as

$Ao+B=\{w|w_1$inA,$w_2$inB,$|w_1|=|w_2|,$ and $w=w_{1}o+w_2\}$

Show that the class of regular languages is closed under XOR. That is$,$ if A and $B$ are regular

languages, then $Ao+B$ is a regular language.