Consider the two regular expressions

$R=0^{**}+1^{**}$

$S={01}^{**}+{10}^{**}+1^{**}0+(0^{**}1{)}^{**}$

$($a$)$ Find a string in $L\frac{R}{\frac{?}{?}}L(S).$

$($b$)$ Find a string in $L\frac{S}{\frac{?}{?}}L(R).$

$($c$)$ Find a string in $L(R)L(S).$

$($d$)$ Find a string in $\frac{?}{\text{b}\text{a}\text{r}}(L(R)L(S)).$