Problem 4 (Sipser Problem 1.42). 1.42 For languages
A
and
B
, let the shuffle of
A
and
B
be the language
{(w|w
|
=a_(1)b_(1)cdotsa_(k)b_(k)):}
, where
a_(1)cdotsa_(k)inA
and
b_(1)cdotsb_(k)inB
, each
{:a_(i),b_(i)in\Sigma ^(**)}
. Show that the class of regular languages is closed under shuffle.