Find CFG$\text{'}$s and Regular Grammer that generate these regular languages over the alphabet

S$=\{$a$,$ b$\}$:

$1.$ The language defined by $($aaa $+$ b$)*$

$2.$ The language defined by $($a $+$ b$)*($bbb $+$ aaa$)($a $+$ b$)*$

$3.$ All strings without the substring aaa.

$4.$ All strings that end in b and have an even number of b$\text{'}$s in total.

$5.$ The set of all strings of odd length.

$6.$ All strings with exactly one a or exactly one b$.$

$7.$ All strings with an odd number of a$\text{'}$s or an even number of b$\text{'}$s$.$

For the following CFG$\text{'}$s find regular expressions that define the same language

and describe the language.

$8.$ S$--$aX bS aIb

X$--$ aX a

$9.$ S$-$ bS aX b

X$--$ bX aS a

$10.$ S$-$ aaS abSIbaSlbbSIA

$11.$ S$-$ aB IbA I A

A $--$ aS

B $--$ bS

$12.$ S$-$ aB bA

A $--->$ aB a

B $-->$ bA b

$13.$ S$-$ aS bX a

X$--$ aX bY a

Y$-->$ aY a

$14.$ S$-->$ aS bXl a

X$---$ aXI bY bZ a

Y$->$ aY a

Z$--->$ aZ bW

W $-->$ aW a

$15.$ S$-$ bS aX

X$--->$ bS I aY

Y$-$raYlbYla lb

$16.($i$)$ Starting with the alphabet

S$=\{$ab$()+*\}$

find a CFG that generates all regular expressions.

$($ii$)$ Is this language regular?