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# Quiz1Solutions.pdf

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School
University of Calgary
Department
Computer Science
Course
CPSC 233
Professor
Tony Tang
Semester
Winter

Description
1 MATHEMATICS 271 L02 WINTER 2014 QUIZ 1 Thursday, January 30, 2014 Duration: 30 minutes STUDENT ID# [5] 1. Write the negation of each of the following statements. Note that the answer \It is not the case that:::" is not acceptable. 2 (a) There exists an integer n such that n + n is odd. Solution: For every integer n, n + n is even. (b) For all real numbers x, there exists a real number y such that bx+yc = bxc+byc. Solution: There exists a real number x such that for every real number y, bx + yc =6 bxc + byc. (c) For all integers a;b, and c, if a is prime and ajbc, then ajb or ajc. Solution: There exist integers a;b, and c so that a is prime and ajbc and a6 jb and a6 jc. (d) There exists an integer m such that for all integers n, m + n is even. Solution: For every integer m there exists and integer n such that m + n is odd. (e) For every positive real number ", there exists a rational number r such that for every integer m, jm ▯ rj < ". Solution: There exists a positive real number " such that for every rational number r there exists an integer m such that jm ▯ rj ▯ ". 2
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