# Math Help - Equivalent Relations and Partition.

1. ## 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.

2. 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.