Question: Form an argument that proves the following multi-part proposition addressing what feels like a distributive-type property of the power set constructor with with the union

Form an argument that proves the following multi-part proposition addressing what feels like a

distributive-type property of the power set constructor with with the union and intersection of sets.

Proposition.

Suppose that A and B are sets

P(A)P(B)P(AB)with equality holding if and only if one of A or B is a subset of the other.

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