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In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric, transitive. 1) Let A = { set of all people }, relation R: A xA where R = { (a,b) | a,b EA, a is at least as tall as b}

In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric, transitive. 1) Let A = { set of all people }, relation R: A xA where R = { (a,b) | a,b EA, a is at least as tall as b}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric, transitive. 1) Let A = { set of all people }, relation R: A x A where R= { (a,b) | a,bEA, a is at least as táll as b} 2) Set S = {0,1,2,3}, relation R: Sx S is'defined as: (m,n) ER if m + n = 4; 3) Z is the set of integers. Relation R: Zx Z is defined as: x,y e Z; (x,y) E R, x is a multiple of y; 4) Z* is the set of positive integers, relation R: Z*x Z*, a,b,c,de Z*; (a,b).(c,d) ER if an only if a +d = b + c. 5) R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3).(2,4),(3,1)}; S = {(2,1}.(3,1).(3,2).(4,2)}. Find So R, R o S, R1, S1,where o means composition.
Transcribed Image Text:In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric, transitive. 1) Let A = { set of all people }, relation R: A x A where R= { (a,b) | a,bEA, a is at least as táll as b} 2) Set S = {0,1,2,3}, relation R: Sx S is'defined as: (m,n) ER if m + n = 4; 3) Z is the set of integers. Relation R: Zx Z is defined as: x,y e Z; (x,y) E R, x is a multiple of y; 4) Z* is the set of positive integers, relation R: Z*x Z*, a,b,c,de Z*; (a,b).(c,d) ER if an only if a +d = b + c. 5) R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3).(2,4),(3,1)}; S = {(2,1}.(3,1).(3,2).(4,2)}. Find So R, R o S, R1, S1,where o means composition.
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