Please define the regular expression for the set $\{$a$,$b$\}.$ It has only two letters a and b$.$

$$Questions are given belowPROBLEMS

All words that contain exactly two $b\text{'}$s or exactly three $b\text{'}$s$,$ not more.

$($i$)$ All strings that end in a double letter.

$($ii$)$ All strings that do not end in a double letter.

All strings that have exactly one double letter in them.

All strings in which the letter $b$ is never tripled. This means that no word contains the

substring $bbb.$

All words in which $a$ is tripled or $b$ is tripled, but not both. This means each word con$-$

tains the substring aaa or the substring $bbb$ but not both.

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

$($ii$)$ All words that do not have both the substrings bba and abb.

All strings in which the total number of $a\text{'}$s is divisible by $3$ no matter how they are dis$-$

tributed, such as aabaabbaba.