$1\mathrm{.}1.$ Use the same ideas to describe an automaton for the following task. Most Russian female last names end in a letter $"$a$".$ Describe an automaton for recognizing words that end in $"$a$".$ For example, "Ivanov" should be rejected, but "Ivanova" or "IVANOVA" should be accepted.

A natural idea is to have $3$ states:

the start state $S,$

the state A indicating that the last read letter was $"$a$"$ or $"$A$",$ and

the state $D$ indicating that the last read letter was different from $"a"$ and $"A".$

Start is the starting state, A is the only final state. The transitions are as follows:

from S$,$ letters $"$a$"$ and $"$A$"$ lead to state A$,$ any other letter leads to state D;

from A$,$ letters $"$a$"$ and $"$A$"$ lead to state A$,$ any other letter leads to state D;

from D$,$ letters $"$a$"$ and $"$A$"$ lead to state A$,$ any other letter leads to state D$.$