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    Discrete Mathematics and Equivalence Classes

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    Let X={1,2,3,4,5}, Y={1,2}.
    Define relation R on g(x) by ARB iff AY =BY
    *Note: g(x) is the power set of x and R is a equivalence relation (no need to prove this)*

    a) C={2,3}. List the elements of [C], the equivalence class containing C.
    b) How many distinct equivalence classes are there?
    c) Suppose X={1,2,...,n}, n2, Y and R the same as above.
    How many equivalence classes are there, in terms of n?
    d) Suppose X={1,2,...,n}, n2, and Y={1,2,...,m}, mn. R the same as above.
    How many equivalence classes are there, in terms of n?

    © BrainMass Inc. brainmass.com October 10, 2019, 3:53 am ad1c9bdddf
    https://brainmass.com/math/discrete-math/discrete-mathematics-equivalence-classes-440225

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    This solution determines the number of equivalence classes in terms of n.

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