a4 - Concordia University Department of CSE COMP 232...

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Unformatted text preview: Concordia University Department of CSE COMP 232 Mathematics for Computer Science Assignment 4 1. Use strong induction to prove that for every integer n 8 there exist non-negative integers x,y such that n = 3 x + 5 y . 2. The Fibonacci numbers are defined as follows: f = 0 ,f 1 = 1, and f n +2 = f n + f n +1 whenever n 0. Prove that when n is a positive integer: f- f 1 + f 2 + ...- f 2 n- 1 + f 2 n = f 2 n- 1- 1 3. (10 marks) For each of the following relations on the set Z of integers, determine if it is reflexive, symmetric, anti-symmetric, or transitive. On the basis of these, state whether or not it is an equivalence relation and/or a partial order. (a). R = { ( a,b ) | a 2 = b 2 } (b). S = { ( a,b ) | | a- b | 1 } 4. A relation R on a set A is said to be irreflexive if for every a A , ( a,a ) / R . Which of the following relations on Z are irreflexive? Give reasons for your answers....
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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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a4 - Concordia University Department of CSE COMP 232...

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