# Equivalent Relations and Partition.

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• Feb 1st 2010, 02:50 PM
iMoons
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.
• Feb 1st 2010, 03:02 PM
Plato
Quote:

Originally Posted by iMoons
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.