$3\mathrm{.}48.$ Explicitly give von Neumann$$s definition of $4$ and $5$ in terms of sets.

A set SSS is called transitive if and only if every element of an element of SSS is itself an element of SSS$.$ In other words, SSS is called transitive if and only if A in BA $\backslash$in BA in B and B in SB $\backslash$in SB in S implies A in SA $\backslash$in SA in S$.$ The notion of a transitive set should not be confused with a transitive relation.