1. The problem statement, all variables and given/known data Assume that D is a transitive set. Let B be a set with the property that for any a in D, a is a subset of B implies a is an element of B. Show that D is a subset of B. 3. The attempt at a solution My first step is to show that the empty set must be an element of D if D is non-empty. (D = 0 is an easy case since its trivially a subset of B) By the regularity axiom there must be some element c such that c intersect D = empty But since D is transitive it must contain all elements of c thus c must be empty. Since the empty set is a subset of B it implies the empty set is and element of B since the empty set is an element of D. I'm a little stuck on how to continue from here, any ideas?