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Math Help - Equivalent Relations and Partition.

  1. #1
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    Equivalent Relations and Partition.

    How many equivalence relations can be defined on S={a,b,c}?

    3square = 9

    How many partitions can be defined on S={a,b,c}?

    not sure about this.
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  2. #2
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    Quote Originally Posted by iMoons View Post
    How many equivalence relations can be defined on S={a,b,c}?
    There is a one-to-one correspondence betweens equivalence relations on a set and partitions of that set.
    You want the Bell number corresponding to the cardinality of the set.
    Do a web search for Bell numbers.
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