24 - Review.txt

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December 2 2014
ETLC 2-001
Equivilance relations
R on A
Partitions A by R,
Every element in each partiion is related.
Relations on {1,2,3,4,5,6}
e.g.: {{1},{2},{3,5},{4,6}}
R = {(1,1), (2,2), (3,3), (3,5), (5,3), (5,5),
(4,4), (4,6), (6,4), (6,6)}
Equivilance class
example
[1] = {1}
[2] = {2}
[3] = {3, 5}
[4] = {4, 6}
[5] = {3, 5}
[6] = {4, 6}
[x] =
Partitions = {[1], [2], [3], [4], [5], [6]}
= {{1}, {2}, {3,5}, {4,6}}
Partitions induced by a relations means the set
of equivilance classes.
R on x1 = x2
reflexive:
(x1, y1),(x2,y2)^2, (x1, y2) R (x2, y2) x2 = x1
Is Symmetric
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