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h3 - D q =(1 2-q 1 2 q Find q ∈ Q D q and ± q ∈ Q D...

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HOMEWORK 3 Question 1. Let A and B be any sets. Prove that ( A B ) r ( A B ) = ( A r B ) ( B r A ) . Question 2. For each of the following statements, give either give a proof or give a counterexample. (a) Let A , B and C be any sets. Then A ( B r C ) = ( A B ) r ( A C ) . (a) Let A , B and C be any sets. Then A ( B r C ) = ( A B ) r ( A C ) . Question 3. (a) For each q Q + , let
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Unformatted text preview: D q = (1 / 2-q, 1 / 2 + q ). Find [ q ∈ Q D q and ± q ∈ Q D q . (b) For each q ∈ Q , let K q = Rr { q } . Find [ q ∈ Q K q and ± q ∈ Q K q . Question 4. Let A and B be any sets. Prove that P ( A ) ∪ P ( B ) ⊆ P ( A ∪ B ) . 1...
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