Question 3. d) Kripke Structures - Universal Predecessors

The universal predecessors of p & !q has been written as a & p. But shouldn't universal predecessors also include Deadends? The deadends here are {}, {q}, {p} and {pq}. And the predecessors of state p & !q are {pqa} and {pa}. Should we not have a formula satisfying all these states since a & p does not satisfy deadends.