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    Equivalence Relations and Classes

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    Let L be a subset of {a,b}*
    Define a relation R (R sub L) on S* as follows:
    L

    for All of x, y is a member of S*,
    (x,y) are members of R if for all of z, xz are members of L iff yz are members of L

    A) Show that R is an equivalence relation

    B) Suppose L={a^i b^i where i >= 0}
    What can you say about the index of R (number of classes)? is it finite or infinite?
    Show some classes and elements in these classes to justify your answer?

    c) Suppose L={a^i b^j where i,j >= 0}
    What can you say about the index of R (number of classes)? is it finite or infinite?
    Show some classes and elements in these classes to justify your answer?

    D) Suppose L={a^i b^3i where i >= 0}
    What can you say about the index of R (number of classes)? is it finite or infinite?
    Show some classes and elements in these classes to justify your answer?

    Note: ^ means to the power, so a^i means a to the power of i.

    © BrainMass Inc. brainmass.com November 29, 2021, 11:58 pm ad1c9bdddf
    https://brainmass.com/math/discrete-structures/equivalence-relations-classes-12978

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    First, let's clarify the definitions.
    is a set of sequences of 's and 's. If we can define multiplications for and , then . is a subset of . The relation defined ...

    Solution Summary

    Equivalence relations and classes are investigated. The solution is well presented.

    $2.49

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