Explore BrainMass

Explore BrainMass

    Equivalence Classes

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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'''?

    © BrainMass Inc. brainmass.com March 4, 2021, 5:49 pm ad1c9bdddf
    https://brainmass.com/math/recurrence-relation/equivalence-class-relations-12967

    Attachments

    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.

    $2.49

    ADVERTISEMENT