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Family of sets

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Suppose F is a family of sets. Prove that there is a unique Set A that has the following two properties.
a) F is a subset of P(A) and
b) For all of B (F is a subset of P(B) then A is a subset of B

Should use an upset down A for all of B.
For the word then an arrow should be used.

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This solution shows how to assess a family of sets.

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