$1\mathrm{.}41$

For languages A and $B,$ let the perfect shuffle of A and $B$ be the language

$\{\begin{array}{c}w|w=a_1{b}_{1}dots{a}_k{b}_k\end{array},$ where $a_{1}dots{a}_k$inA and $b_{1}dots{b}_k$inB, each $\{$:$a_{i,},b_{i}in\}$

Show the class of regular languages is closed under perfect shuffle.

please make the answer readable and easy to follow