# a2 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE...

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DEPARTMENT OF COMPUTER SCIENCE AND SOFTWARE ENGINEERING COMP232 MATHEMATICS FOR COMPUTER SCIENCE ASSIGNMENT 2 FALL 2011 Due Date: Thursday October 20 at midnight 1. Prove that if x 5 is irrational then x is irrational, by proving the contrapositive. 2. Give a proof by cases to show that there are no integer solutions to the equation 2 x 2 + 5 y 2 = 14 . 3. Give a proof by contradiction to show that the cube root of 3 is an irrational number. 4. Give a proof by contradiction to show that if the integers 1, 2, ··· , 99, 100 , are placed randomly around a circle (without repetition), then there must exist three adjacent numbers along the circle whose sum is greater than 152. 5. Prove the following by contradiction: (a) There is no least positive rational number. (b) For all real numbers x and y , if x is irrational and y is rational then x y is irrational. (c) log 5 (2) is irrational. 6. Let

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## This note was uploaded on 01/05/2012 for the course COMP 232 taught by Professor Tba during the Spring '11 term at Concordia Canada.

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a2 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE...

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