this solution is still wrong

Question

could you explain what I am doing wrong

Answer 1

Remove the deadend initial states (as done in a)), then get the reachable states (b)), and after that clear the transition relation from deadends (c)) and unreachable states (d)).

Comments

thanks I was able to solve (b) with your help but I have a question regarding the format for (c) and (d) next(p) and next(q) will be true when there is a transition from to a state that has p true and q true is this right ?

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Right! For the transition relation, you double all variables. You then have un-primed and primed variables. Each assignment corresponds to a pair of a state (un-primed variables) and a next state (primed variables). There exists a transition from the state to the next state iff the assignment is a satisfying assignment of the transition relation formula.