Given $R=b^{**}(b{a}^{+}{a}^{+}{)}^{+}{b}^{**}$ 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 $001.[3$ marks$]$

f$)$ Design a regular expression that accepts the language of all binary strings which their length is odd with no occurrences of $11.[3$ marks$]$