Find CFG$\text{'}$s for the following languages over the alphabet $=\{a,b\}.$

$($i$)$ All words in which the letter $b$ is never tripled.

$($ii$)$ All words that have exactly two or three $b\text{'}$s$.$

$($i$)$ All words that do not have the substring $ab.$

$($ii$)$ All words that do not have the substring baa.

All words that have different first and last letters:

$\{abba,$abbabb $ba$ bbadots$\}$

Consider the CFG:

$SAA$

$A$AAA

$AbA|Ab|a$

Prove that the language generated by these productions is the set of all words

with an even number of $a\text{'}$s$,$ but not no $a\text{'}$s$.$ Contrast this grammar with the

CFG in Problem $5.$

Describe the language generated by the following CFG:

$SSS$

$Sxxx$

$xax|xa|b$