CODEWITHSUNDEEP
functiondiscrete-mathematics
user3562937
user3562937

Reputation: 31

How can I calculate the number of equivalence classes of this relation?

Let S = {1,2,3,....,8}. Consider the power set X = P(S) and the equivalence relation on X according to which two elements of X are equivalent if they have the same size. How many equivalence classes are there?

Upvotes: -1

Views: 8358

Answers (2)

Arijit Ghosh
Arijit Ghosh

Reputation: 57

Those who are frustrated searching how to find number of equivalence classes here you go:

Number of equivalent classes is equal to number of state in minimal DFA.

Upvotes: 0

templatetypedef
templatetypedef

Reputation: 373452

Each equivalence class of this relation will consist of a collection of subsets of X that all have the same cardinality as one another. Since |X| = 8, there are 9 different possible cardinalities for subsets of X, namely 0, 1, 2, ..., 8. Therefore, there are 9 different equivalence classes.

Hope this helps!

Upvotes: 1

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