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Unformatted text preview: Data Structures and Algorithms Homework Assignment 2 Given: January 25, 2011 Due: February 03, 2011 This assignment is due by the end of the class on the due date. Unless all problems carry equal weight, the point value of each problem is shown in [ ]. To receive full credit all your answers should be carefully justified. Each solution must be the students own work. Assistance should be sought or accepted only from the course staff. Any violation of this rule will be dealt with harshly. 1. Prove that the following propositions are true. The sum of any rational number and any irrational number is irrational. 2. Given any numbers x,y and z , if x y is odd and y z is even, is x z odd or even? Prove your claim. 3. Prove or disprove the following. Among five integers there are always three with sum divisible by 3. 4. Prove that for all integers n , if n 3 is divisible by 4 then n 2 1 is divisible by 8....
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