Each of the following languages is the union or intersection of two simpler languages. In each part, construct DFAs

for the simpler languages, then combine them using the construction discussed in class to give the state diagram of

a DFA for the language given. Delete the states that cannot be reached from the start state. In all parts, $\backslash$Sigma $=\{0,1\}.$

$(1)\{$w$|$w contains an even number of $0$s or contains exactly two $1$s$\}$

$(2)\{$w$|$w starts with an $0$ and has at most one $1\}$