$(15$ points$)($a$)2$inA.

If xinA, then $x^2$inA.

Based on the above recursive definition, describe $A$ in at most two sentences.

$($b$)inB.$

If yinB, then $\text{'}0\text{'}{y}^{s}0\text{'}$ inB and $y^{\text{'}}{1}^{\text{'}}$yinB.

Write down any five non$-$empty strings in $B.$

Use at most two sentences to describe the elements of $B.$