# Equivalence Classes

Let P, P' be equivalence relations on a set A. Let n, n' be the number of equivalence classes of p, p', respectively.

A) define an equivalence relation p'' as follows:

xp''y <=> (xpy) and (xp'y)

what is the least number of equivalence classes of p''? What is the greatest number of equivalence classes of p''?

B)define an equivalence relation p''' as follows:

xp'''y <=> (xpy) or (xp'y)

what is the least number of equivalence classes of p'''? What is the greatest number of equivalence classes of p'''?

https://brainmass.com/math/recurrence-relation/equivalence-class-relations-12967

#### Solution Preview

A.)

Because, in set theory, and means intersection. Therefore, the number of equivalence classes of p'' will be equal to the intersection of n and n' classes.

Hence, if all n (of p) and n' (p') equivalence classes are completely disjoint, in that case the number of equvalence classes of p'' will be ...

#### Solution Summary

Equivalence classes are found from equivalence relations. The greatest number of equivalence classes of p is determined.