Only send answers writtten on paper, need written answers only.

$3\mathrm{.}7.$ Find a regular expression corresponding to each of the following subsets of $\{a,b{\}}^{**}.$

a$.$ The language of all strings containing exactly two $a\text{'}$s$.$

b$.$ The language of all strings containing at least two $a\text{'}$s$.$

c$.$ The language of all strings that do not end with $ab.$

d$.$ The language of all strings that begin or end with $aa$ or $bb.$

e$.$ The language of all strings not containing the substring $aa.$

f$.$ The language of all strings in which the number of $a\text{'}$s is even.

g$.$ The language of all strings containing no more than one occurrence of the string $aa.($The string aaa should be viewed as containing two occurrences of $aa.)$

h$.$ The language of all strings in which every $a$ is followed immediately by $bb.$

i$.$ The language of all strings containing both $bb$ and aba as substrings.

j$.$ The language of all strings not containing the substring aaa.

k$.$ The language of all strings not containing the substring bba.

The language of all strings containing both bab and aba as substrings.

$m.$ The language of all strings in which the number of $a\text{'}$s is even and the number of $b\text{'}$s is odd.