# hw1 - A3. (a) Let q be an integer. Prove that if 3 divides...

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Assignments for Math 140A, Fall 2011 Problem Set 1. Due Friday, September 30 Rudin, Chapter 1, pp 21-22: #1, #4, #5 Also do the following problems: A1. If A , B , and C are subsets of X , prove (carefully) that ( A \ B ) ( C \ B ) = ( A C ) \ B ) Notation: ( A \ B ) = { x A : x 6∈ B } . A2. For x and y any real numbers, prove that ± ± | x | - | y | ± ± ≤ | x - y | You may use Theorem 1.37 in the text.
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Unformatted text preview: A3. (a) Let q be an integer. Prove that if 3 divides q 2 , then 3 divides q . (Do not use unique factorization of integers into prime powers.) Hint: If 3 does not divide q , then q = 3 k + r , with r = 1 or r = 2. (b) Prove that there is no rational number r for which r 2 = 3. 1...
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## This note was uploaded on 09/30/2011 for the course MATH 140a taught by Professor Staff during the Fall '08 term at UCSD.

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