$1\mathrm{.}4$ Each of the following languages is the intersection of two simpler languages. In

each part, construct DFAs for the simpler languages, then combine them using the

construction discussed in footnote $3($page $46)$ to give the state diagram of a DFA

for the language given. In all parts, $=\{a,b\}.$

a$.$ has at least three a$\text{'}$s and at least two b$\text{'}$s ca