Question $38$

$S$ is a set of strings over the alphabet $\{a,b\}$ and is defined recursively as follows:

Basis: $inS$ and binS

Recursive rules: If $x$ is in $S,$ then bxainS and axbinS.

Select the set that corresponds to all the strings in $S$ of length $4.$

$[$bbaa$,$ aabb$)$

$[$baba$,$ abab$]$

$$

$[$bbaa$,$ aabb, baba, abab$]$