2By A'2, every set y satisfying axiom A' must be a transitive set. But it is not true that every set y satisfying axiom A must be transitive. So, it seems natural to ask the following. Question 2: (i) If a set y satisfies axiom A, is it necessary that the transitive closure of y is a set satisfying axiom A? (ii) If x is a transitive set, does any set y satisfying the axiom A and having x as a member set be a transitive set ?
