Question $1$: Give state diagrams of DFAs recognizing the following languages. In all parts, $\backslash$Sigma $=\{$a$,$b$\}.$

$1.\{$w$|$ w has length at least $3$ and its third symbol is a b$\}$

$2.\{$w$|$ w starts with b and has even length, or starts with a and has odd length$\}$