Given $R=(0^{**}{10}^{+}{)}^{**}(1)$ and $S=(1^{**}{01}^{+}{)}^{**}.$

$($a$)$ Give an example of a string that is neither in the language of $R$ nor in S $.$

$[2$ marks$]$

$($b$)$ Give an example of a string that is in the language of $S$ but not R $.$

$[2$ marks$]$

$($c$)$ Give an example of a string that is in the language of $R$ but not S $.$

$[2$ marks$]$

$($d$)$ Give an example of a non$-$empty string that is in the language of R and S $.$

$[2$ marks$]$

$($e$)$ Design a regular expression that accepts the language of all binary strings with no occurrences of $"010".$

$[2$ marks$]$