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Unformatted text preview: MATH 74 MIDTERM 2 1. Short reponse: 20 points For any set S , let P ( S ) denote the set of all subsets of S . 1. [4 pts] Give an example of sets A and B such that P ( A B ) 6 = P ( A ) P ( B ) . You do not need to prove that your sets A and B have this property; you just need to specify what A and B are. 2. [4 pts] Let A = { 1 , 2 , 3 } . Give an example of an element Z of P ( A A ) that is not of the form B C , with B and C subsets of A . You do not need to prove that your Z has this property. You just need to specify what Z is. 3. [4 pts] Give an example of a function f : Z Z that is injective but not surjective. You do not need to prove that f has these properties. You just need to specify the rule of f . 4. [4 pts] Give an example of a function g : R R that is surjective but not injective. You do not need to prove that g has these properties. You just need to specify the rule of g ....
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This note was uploaded on 02/10/2010 for the course MATH 74 taught by Professor Courtney during the Fall '07 term at University of California, Berkeley.
 Fall '07
 COURTNEY
 Sets

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