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(a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p,p), (p, q), (q, r), (r, s), (r,r), (s,r)}. This relation is not reflexive. What element(s) would we need to add to R in order for it to be reflexive? (b) Consider the relation R on the set A = (X,Y,Z) defined by R = {(X, X), (X,Y), (X, Z), (Y, Y), (Y,Z), (Z, X)}. This relation is not symmetric. What element(s) would we need to add to R in order for it to be symmetric? (c) Consider the relation R on the set A = {X,Y,Z} defined by R= {(X,Y), (Y, X), (Z, Z)}. This relation is not transitive. What element(s) would we need to add to R in order for it to be transitive?

(a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p,p), (p, q), (q, r), (r, s), (r,r), (s,r)}. This relation is not reflexive. What element(s) would we need to add to R in order for it to be reflexive? (b) Consider the relation R on the set A = (X,Y,Z) defined by R = {(X, X), (X,Y), (X, Z), (Y, Y), (Y,Z), (Z, X)}. This relation is not symmetric. What element(s) would we need to add to R in order for it to be symmetric? (c) Consider the relation R on the set A = {X,Y,Z} defined by R= {(X,Y), (Y, X), (Z, Z)}. This relation is not transitive. What element(s) would we need to add to R in order for it to be transitive?

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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(a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p, P), (p, q), (q, r), (r, s), (r,r), (s,r)}. This relation is not reflexive. What element(s) would we need to add to R in order for it to be reflexive? (b) Consider the relation R on the set A = {X, Y, Z} defined by R = {(X, X), (X,Y), (X, Z), (Y, Y), (Y,Z), (Z, X)}. This relation is not symmetric. What element(s) would we need to add to R in order for it to be symmetric? (c) Consider the relation R on the set A = {X,Y,Z} defined by R= {(X,Y), (Y, X), (Z, Z)}. This relation is not transitive. What element(s) would we need to add to R in order for it to be transitive?
Transcribed Image Text:(a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p, P), (p, q), (q, r), (r, s), (r,r), (s,r)}. This relation is not reflexive. What element(s) would we need to add to R in order for it to be reflexive? (b) Consider the relation R on the set A = {X, Y, Z} defined by R = {(X, X), (X,Y), (X, Z), (Y, Y), (Y,Z), (Z, X)}. This relation is not symmetric. What element(s) would we need to add to R in order for it to be symmetric? (c) Consider the relation R on the set A = {X,Y,Z} defined by R= {(X,Y), (Y, X), (Z, Z)}. This relation is not transitive. What element(s) would we need to add to R in order for it to be transitive?
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