Construct FSM

Question

Please could someone explain in exam 2019.08.27 problem 3 part a?

Thanks in advance.

Answer 1

1) if we have p = 0  q=0 we get :

=(p V q) <-->p' & ( !p <--->q') &a

=0   <---> p' &( !p <--->q') &a

=!(p' & (!P &(1<--->q') & a

=!p' & q' &a

2) if we have p=0   q= 1 we get :

=1 <----> p' & (!p<-->q') &a 

=p' & (1<--->q') &a

=p' & q' &a

3) if we have  p=1 q=0 we get :

=p' & (!p <--->q')&a

=p' & ( !p <---> q') &a

=p' & !q' & a

4) if we have p=1 q=1 we get :

=p'& (!p <---> q') &a

=p' & !q' & a