Unformatted text preview: b. x ∈ ∪F \ ∩G ; here F and G are families of sets. c. x ∈ u i ∈ I ( A i ∩ B i ); here each A i and B i is a set, and I is an index set. d. x ∈ ∪{P ( A )  A ∈ F} ; here F is a family of sets. 3 Show that ( ∩F ) ∩ ( ∩G ) = ∩ ( F ∪G ); here F and G are families of sets. 4 Let us deFne A = ∅ . Then for each n ≥ 1, let A n = A n1 ∪ { A n1 } . Please don’t freak out: this is not a potential exam problem (yet). a. Write out A 1 , A 2 , and A 3 . b. What is  A n  ? c. DeFne A ω = u n ∈ N A n . What is  A ω  ? d. Make a sensible deFnition for A ω +1 . What is  A ω +1  ? Is this set equal to A ω ? Why or why not? e. Make a sensible deFnition for A 2 ω ....
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 Fall '09
 LARSON
 Logic, Will Rogers, Aω, logical forms, c. Deﬁne Aω

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