$14\mathrm{.}3$: A Minimal DFA?

Let$=\{$a$,$ b$\}$ and let M be the following DFA over$.$ The state set is $\{1,2,3,4\},$ the start state is $1,$ the final state set is $\{2,3\},$ and the transition function has$$$(1,$ a$)=2,$$(1,$ b$)=3,$$(2,$ a$)=3,$$(2,$ b$)=4,$$(3,$ a$)=4,$$(3,$ b$)=2,$$(4,$ a$)=2,$ and$$$(4,$ b$)=3.$ Then M is the minimal DFA for its language.