$.$ For below DFAs give equivalent regular expressions: $(15$ points$)$

Q$2.$ Find the minimum pumping length for the following languages. $(15$ points$)$

A$=\{0^*101^*\}$

B$=\{10^*1\}$

A $\backslash$cup B

C$=\{(01)^*\}$

D$=\{\}$

Q$3.$ For any language A let A$^$R$=\{$w$^$R $|$w in A$\}.$ Show that if A is regular then so is A$^$R$.(10$ points$)$

Q$4.$ Minimize the states of the DFA below: $(10$ points$)$

Q$5)$ Given the following regular expression: $(15$ points$)$

r $=($ab $+$ ba$)*($aa $+$ bb$).$ Give the DFA and the

minimised DFA of the regular expression.