hmk4 - COT 3100 Homework#4 Fall 00 Lecturer Arup Guha...

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COT 3100 Homework #4 Fall ’00 Lecturer: Arup Guha Assigned: 10/17/00 Due: 10/24/00 (No late assignments) 1) Prove or disprove: If a relation R, defined as a subset of A x A, is transitive, then R ° R is transitive as well. 2) Define sumdigits(a), where a is a positive integer, to be the sum of the digits in the decimal representation of the positive integer a. Using this definition of the function sumdigits, consider the following relation: {(a,b) | a Z + b Z + (a b sumdigits(a) sumdigits(b)} Determine if this relation is (i)reflexive, (ii)irreflexive, (iii)symmetric, (iv)antisymmetric, and (v)transitive? The rest of the questions will be based on the following definitions. (Note: Prove your answer to questions 3, 4, or 5 through a valid proof or a disproof using a counter-example.) Definition. Let R A × A denote a binary relation. The following relations defined over A are called closures : (a) The reflexive closure of R is r ( R ) = R {( a , a ) | a
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This document was uploaded on 06/09/2011.

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