I'm using the definition of a full binary tree which is a graph where there is exactly one path between any two vertices, there is a root, and where every vertex has either two children or none at all.(adsbygoogle = window.adsbygoogle || []).push({});

If I had the following graph:

*

that is, just the root, then could I construct the following set to represent this:

{{}} -- (i.e. the set containing the empty set a.k.a. the full binary tree containing a vertex with NO children)

And could the graph

........*

......./.\

...../.....\

...*.......*

.........../.\

........./.....\

.......*.......*

be represented by

{{},{{},{}}}

Basically I was wondering if I could construct all of the Zermelo-Fraenkel set theory axioms for a class of objects which were strictly full binary trees. I guess that I would be using the Extension axiom to construct the two sets that I have just given?

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# Homework Help: Representing Sets as Binary Trees

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