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 quivalence classes of p''? What is the greatest number of quivalence classes of p''?
B)define an equivalence relation p''' as follows:
xp'''y <=> (xpy) or (xp'y)
what is the least number of quivalence classes of p'''? What is the greatest number of quivalence classes of p'''?
Mathematics Homework Solutions
#12967
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'''?
Equivalence classes are found from equivalence relations.
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