Given R$=$b$($ba $+$U a $+)+$b $$ and S$=($a$$ba$+$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$]$