$[10$ Points$]$ The following is a transition diagram for a DFA over the alphabet $=$

$\{0,1\}.$ Answer the following questions about this automaton:

$($a$)$ What is the start state? What is the set of accept states?

$($b$)$ What is the sequence of states the DFA goes through on input $101100?$

$($c$)$ Does the machine accept every string $w$ that contains exactly two $1$s$?$ Why or

why not?

$($d$)$ Does the machine reject every string $w$ that has odd number of $0$ s$?$ Why or why

not?

$($e$)$ Describe the language accepted by the machine using the set builder notation.