Hello I need help solving these two Finite State Machine pro

Hello, I need help solving these two Finite State Machine problems. Thank you.

1. For the given FSM, is there anything conditions non-exclusive or conditions incomplete? PressU Holdu Init Wait D- PressD HoldD D tm pulsDm_pulse O A. None B. Press U and Press D are wrong O C. Wait is wrong D. Hold U and Hold D are wrong C.Wait is wrong

Solution

1. Wait is wrong

2. By seeing the figure  the states one might think that S0 and S2 are same but they are not. when input is 1 and state is S1 then the next state is S2, but there is no way of going to S0 from S1 hence S0 and S2 are two different and neccessary states.Also S1 is the state in which output is 1 hence we cant remove S1 as well. Therfore Option is A None.