3202-example - A ( A F A 6 B x A ) We are given that there...

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MHF 2302 Section 2787 Solution to problem 14, page 134 To show: if F is a nonempty family of sets and B is a set, then [ { A \ B | A ∈ F} ⊆ [ ( F \ P ( B )) Proof: We must show, for any x , that if x is in A \ B | A ∈ F} then it is also in S ( F \P ( B )). Now x [ { A \ B | A ∈ F} ↔ ∃ A ∈ F x A \ B ↔ ∃ A ( A ∈ F ∧ x A x 6∈ B ) and x [ ( F \ P ( B )) ↔ ∃ A ( F \ P ( B ))( x A ) ↔ ∃ A ( A ∈ F ∧ A 6∈ P ( B ) x A ) ↔ ∃
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Unformatted text preview: A ( A F A 6 B x A ) We are given that there is a set A such that A F , x A and x 6 B . The last two assertions show that A 6 B , so this A satises A F A 6 B x A , which shows that x is in S ( F \ P ( B ))....
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This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.

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