Adopt the alphabet A $=\{$a$,$ b$,$ c$\}$ and, for each of the following languages, give a regular expression which describes

it$.$

$($a$)$ all strings which do not contain b

$($b$)$ all strings which contain the substring bbb

$($c$)$ all strings in which any b is contained in a substring bb

$($d$)$ all strings in which there is no b appearing further to the right than a c $($thus babbca and aabbb are allowed

but acbcc is not$).$