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Let \(V_0 = \varnothing\) be the empty set and for \(i>0\), let \(V_i = \mathcal{P}(V_{i-1})\), where \(\mathcal{P}(X)\) is the set of all subsets of \(X\) (also known as the power set). So:
\(V_1=\{\varnothing\}\)
\(V_2 = \{\varnothing,\{\varnothing\}\}\)
\(V_3=\{\varnothing,\{\varnothing\},\{\{\varnothing\}\},\{\varnothing,\{\varnothing\}\}\}\)
and so on.
A set \(X\) is called transitive if each element of \(X\) is also a subset of \(X\).
How many elements in \(V_5\) are transitive?
How many elements in \(V_5\) are transitive?