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'''?