Problem $5.(10$ points$)$ Given the event set ${\displaystyle \underset{?}{\overset{?}{}}}=\{a,b,g\},$ construct an FSM that

has the following set of marked languages:

a$)$ Marked language: $\{abg,$abb,$bbg\}$

$(3$ points$)$

b$)$ Marked language denoted by $(ab{)}^{*}g$

$(3$ points$)$

c$)$ Marked language denoted by $a(ba{)}^{*}{a}^{*}$

$(4$ points$)$