PLEASE DRAW THE STATE DIAGRAMS

$3.(20$ points$)$ Please give the state diagram of a DFA for the language given. In all parts, $\backslash$Sigma $=\{$a$,$ b$\}.$

$(1)\{$w$|$ w has an even number of a$$s$\}$

$(2)\{$w$|$ w has one or two b$$s$\}$

$(3)\{$w$|$ w has even length$\}$

$(4)\{$w$|$ w has an odd number of a$$s$\}$

Your solution should be a DFA solution.

Lecture: RL$-$RE

$4.$ Give regular expressions that describe the languages. In all parts, the alphabet is $\{0,1\}.(20$ points$)$

For the correct format, please check our examples in slides and use the following symbols: $0,1,,*,(),$ U$.$

Other formats like this $^1(0+1)*$$ will not be graded.

a$.\{$w$|$ w starts with $0$ and has an odd length$\}$

b$.\{$w$|$ w starts with $1$ and has an even length$\}$

c$.\{$w$|$ w contains at least two $0$s$\}$

d$.\{$w$|$ w contains at most one $1\}$