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

Basis: $\backslash$lambda in Sandb in S

Recursive rules: If x

is in S

$,$ then bxa in Sandaxb in S

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

Group of answer choices

$\backslash \{$bbaa$,$aabb,baba,abab$\}$

$\backslash \{$bbaa$,$aabb$\}$

$$

$\backslash \{$baba$,$abab$\}$