But still I stuck. I used

p&!q&!a&!next(p)&next(q)& !next(a) | p&q&!a&!next(p)&next(q)& !next(a)

for the answer 1.c but this is also wrong. I understand this. But, what the mistake here? For more clarification I am giving the details below:

Compute the Kripke structure K={I′,S′,R′,L′}of the FSM: A={2Vin,2Vout,I,2Vstate,R}

where Vin={a}, Vout={}, Vstate={p,q}, I=q,

R=p&!a&!next(p)&next(q)|!a&!p&!next(p)&!next(q),

1.a) p&q&!a | !p&q&!a

1.b) p&q&!a | !p&q&!a | !p&!q&!a | !p&q&a | !p&!q&a

a and b answers are correct. But, still can't find the mistake for C and D.

Update:

I have found my mistake. And shared as a different post here!