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Set Theory - Equivalence Classes of an Equivalence Relation

Modern Algebra
Set Theory (III)
Equivalence Classes of an Equivalence Relation

Let ~ be an equivalence relation on a non-empty set A.
Then for any a,b in A
(i) cl(a) is not equal to phi

(ii) Any two equivalence classes cl(a), cl(b) are

either cl(a) intersection cl(b) = phi or, cl(a) = cl(b)

i.e., either cl(a), cl(b) are equal or disjoint.

i.e., two equivalence classes are either equal or have no element in common.

(iii) A = Union cl(a) where a is in A.

The fully formatted problem is in the attached file.

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Solution Summary

Properties of the equivalence classes of an equivalence relation are defined. The solution is detailed and well presented.

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