Given $R=b^{**}(a{b}^{+}{)}^{+}{b}^{**}$ and $S=(a^{**}b{a}^{+}b{)}^{**}$

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 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 $101.$

$[3$ marks$]$

f$)$ Over $=\{1,2,3\}$ design a regular expression that generates all numbers greater than $200.$ For example, $211,33112$ and $1111$ must be generated while $22,111$ and $123$ should not.

$[3$ marks$]$