$7)$ Given $=$

$$

$($

$+)$

$+$

$$ and $=($

$$

$+)$

$$

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 $\backslash$Sigma $=\{1,2,3\}$ 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