Convert the following DFA into a regular expression. Include all steps of conversion.

$5.$ In class we learned with examples that the string s must be chosen carefully to complete the

proof of non$-$regularity using the pumping lemma. In this question, you have to prove, for each

instance below, whether the string s completes the proof of non$-$regularity for language L or

not. Here, p is the pumping length of L assumed for the proof.

$6.$ Give regular expressions generating the following languages over the alphabet $=\{$x$,$y$\}$:

a$)\{$ w $|$ w has the length at least $3$ and its third symbol is x$\}$

b$)\{$ w $|$ w starts with y and has odd length, or starts with x and has even length$\}$

c$)\{$ w $|$ the length of w is at most $6\}$

d$)\{$ w $|$ w is any string except yxy and yy$\}$

e$)\{$ w $|$ w is any string that has third last symbol equal to y$\}$