For unlimited access to Class Notes, a Class+ subscription is required.

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