Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; Az : %3D %3D %3D {2,4, 6}; A3 = {3, 6}. Define the relation R on set A as follows: x R y if and only if {x,y}C A, or {x,y}C A, or {x,y}C A,. That is, x R y if and only if x and y are both in A1 or x and y are both in A2 or x and y are both in A3.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; A2 =
%3D
{2,4, 6}; A3 = {3, 6}.
Define the relation R on set A as follows: x R y if and only if { x, y} C A or { x, y}C A, or { x,y}C A. That is,
x R y if and only if x and y are both in A, or x and y are both in A2 or x and y are both in A3.
Transcribed Image Text:Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; A2 = %3D {2,4, 6}; A3 = {3, 6}. Define the relation R on set A as follows: x R y if and only if { x, y} C A or { x, y}C A, or { x,y}C A. That is, x R y if and only if x and y are both in A, or x and y are both in A2 or x and y are both in A3.
Ris not an equivalence relation. Which property of equivalence does R fail to have? Support your answer with a
specific example.
Transcribed Image Text:Ris not an equivalence relation. Which property of equivalence does R fail to have? Support your answer with a specific example.
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