$[30$ points$]$ Design a finite automaton $($DFA$)$ for each of the following languages over the

alphabet $\{0,1\}.$ Show only the state diagrams, and use as few states as you can.

$3$a$.[10$ points$]\{$w : w either ends with a $1,$ or has no $1$s$\}$

$3$b$.[10$ points$]\{$w : w is one or more $1$s$,$ followed by one or two $0$s$,$ followed by zero or more $1$s$\}$

$3$c$.[10$ points$]\{$w : $|$w$|>=2$ and the last two bits of w are the same as each other$\}$