$1.$ Construcuct the tries for the following sets of keywords:

a$)$ aaa, abaaa, and ababaaa

b$).$ all, fall, fatal, llama and lame

$2.$ draw a transition diagram for unsigned real numbers, for example, $4\mathrm{.}56$

$3.$ provide an DFA that accepts $($a$|$b$)*$