Below is a recursive definition of a set $T.$

Basis: $inT$

Recursive Step: If $sinT,$ then bsinT, sb $b,$ saa inT, asa inT

asainT.

Closure: $sinT$ only if it is $$ or it can be obtained from $$ using finitely many

operations of the Recursive Step.

The only string of length $1$ that belongs to $T$ is $b.$

Two new different elements of the set $T$ are generated in the first execution of

the recursive step.

All of the strings of length up to $3$ inclusive, that belong to the set $T,$ are:

$",$b$,$aa$,$bb$,$baa,aab,aaaa.

T is a set of all strings, over $=\{a,b\},$ containing even number of a$\text{'}$s$.$