MAS111_09_assignment_09 - MAS 111 FOUNDATION OF MATHEMATICS...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 9 HINTS 1. The following two binary relations are defined on the set A = { , 1 , 2 , 3 } . For each relation, determine whether it is reflexive, symmetric, tran- sitive. Give a counterexample in each case in which the relation does not satisfy one of the properties. (a) R 1 = { (1 , 2) , (2 , 1) , (1 , 3) , (3 , 1) } (b) R 2 = { (0 , 0) , (0 , 1) , (0 , 3) , (1 , 1) , (1 , 0) , (2 , 3) , (3 , 3) } Hint : (a) R 1 = { (1 , 2) , (2 , 1) , (1 , 3) , (3 , 1) } is symmetric, but not reflexive (for example, (1 , 1) is not in R 1 ), not transitive (for example, (1 , 2) , (2 , 1) are in R , but (1 , 1) is not in). (b) R 2 = { (0 , 0) , (0 , 1) , (0 , 3) , (1 , 1) , (1 , 0) , (2 , 3) , (3 , 3) } is transitive, but not reflexive ((2 , 2) is not in R ), not symmetric ((2 , 3) is in R , but (3 , 2) is not in). 2. Let R = { (0 , 1) , (0 , 2) , (1 , 1) , (1 , 3) , (2 , 2) , (3 , 0) } . Find R t , the transitive closure of R . Hint : It is easy to use directed graph to find R t . R t = { (0 , 1) , (0 , 2) , (1 , 1) , (1 , 3) , (2 , 2) , (3 , 0) , (0 , 3) , (1 , 0) , (3 , 1) , (1 , 2) , (3 , 2) } . 3. Let S = { (0 , 0) , (0 , 3) , (1 , 0) , (1 , 2) , (2 , 0) , (3 , 2) } . Find S t , the transitive closure of S ....
View Full Document

This note was uploaded on 01/23/2011 for the course MAS 111 taught by Professor Drchansongheng during the Spring '10 term at Nanyang Technological University.

Page1 / 4

MAS111_09_assignment_09 - MAS 111 FOUNDATION OF MATHEMATICS...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online