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

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 ${\displaystyle \underset{?}{\overset{?}{}}}=\{1,2,3\}$ 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$]$