# 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 AY =BY

*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}, n2, Y and R the same as above.

How many equivalence classes are there, in terms of n?

d) Suppose X={1,2,...,n}, n2, and Y={1,2,...,m}, mn. R the same as above.

How many equivalence classes are there, in terms of n?

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

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