Assuming $\backslash$Sigma $=\{$a$,$b$\},$ give $($draw$)$ a finite automaton that recognizes the following languages.

a$)\{$w $|$ w has exactly three a$$s $\}$

b$)\{$w $|$ w has at least three a$$s$\}$

c$)\{$w $|$ w has odd number of a$$s$\}$

d$)\{$w $|$ w has even number of b$$s $\}$

e$)\{$w $|$ w has an odd number of a$$s and ends with one or more b$$s$\}$

f$)\{$w $|$ w has even length and an odd number of a$$s$\}$