Is the power set of x a transitive set?

If X and Y are transitive, then X ∪ Y ∪ { X, Y } is transitive. In general, if X is a class all of whose elements are transitive sets, then { extstyle X\cup \bigcup X} is transitive. X ⊆ P ( X ) . { extstyle X\subseteq {\mathcal {P}} (X).} The power set of a transitive set without urelements is transitive.
Accordingly, when does a set X become a transitive set?
If X is transitive, then is transitive. If X and Y are transitive, then X ∪ Y ∪ { X, Y } is transitive. In general, if X is a class all of whose elements are transitive sets, then is transitive. A set X which does not contain urelements is transitive if and only if it is a subset of its own power set,...
Moreover, when is the ∈ relation of a transitive set? Thus, the ∈ relation is transitive in this case. A transitive set is one in which inclusion " ∈ " is transitive. So A is transitive, if whenever for sets X and Y if Y ∈ X and X ∈ A then Y ∈ A. A is transitive, if whenever the set X ∈ A, it follows that X ⊂ A.
In fact, which is the power set of a set?
Definition In set theory, the power set (or power set) of a Set A is defined as the set of all subsets of the Set A including the Set itself and the null or empty set. It is denoted by P (A). Basically, this set is the combination of all subsets including null set, of a given set.
Furthermore, how to define a relation on a power set?
Let X be a non-empty set and let P ( X) be the power set of X. Let R 3 be the relation defined on P ( X) as follows: ∀ A, B ∈ P ( X), ( A, B) ∈ R 3 if and only if A ≠ B. I've got that it is reflexive because A R 3 A since A ≠ B and A = A therefore reflexive.

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Which is not a transitive relation on a set of people?

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