$(3$ marks$)$ In this question the alphabet is $=\{0,1\}.$ Let $R=(01+001{)}^{**}{0}^{**}$ and

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

$($a$)$ Give two examples of a string $z$ that is both in $R$ and in $S($that is$,$ zinR$S).$

$($b$)$ Give two examples of a string $x$ that is in $R$ and is not in $S($that is$,$ xinR$\frac{}{b}ar(S)$

where $\frac{?}{\text{b}\text{a}\text{r}}(S)$ is the complement of $S).$

$($c$)$ Give two examples of a string $y$ that is in $S$ and is not in $R($that is$,yi\frac{n}{b}ar(R)S).$

In each case briefly explain $($using natural language$)$ why your example strings have the

required property.