For the alphabet $\backslash$Sigma $=\{$a$,$ b$\},$ construct an FA that accepts the following languages.

$($a$)$ L $=\{$all words with exactly one b$\}.$

$($b$)$ L $=\{$all words with at least one a$\}.$

$($c$)$ L $=\{$all words with no more than three b$\text{'}$s$\}.$

$($d$)$ L $=\{$all words with at least one a and exactly two b$\text{'}$s$\}$

$($e$)$ L $=\{$all words with b as the third letter$\}$

$($f$)$ L $=\{$all words with the number of letters being divisible by $4\}$

$($g$)$ L $=\{$all words that do not have two a$$s together or two b$$s together$\}$