(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Set Theory Regulatory Axiom and Ranks

Can you offer guidance or do you also need help?

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