560 views

2 Answers

Best answer
4 votes
4 votes

Number of equivalence relations = number of partitions

Number of partitions can be given by using Bell Number.

For smaller numbers we can construct Bell's triangle by taking B0=B1=1.

Than by taking the last number of the previous row as the starting number in the next row, adding the numbers column wise and writing it next.

eg:

1

1   2

2   3   5

5   7    10   15

B0 = 1

B1= 1

B2= 2

B3= 5

B4= 15

selected by
1 votes
1 votes
No of equivalance classes are nothing but Bell Number.
Bell Number for 3 number is 5.
Answer:

Related questions

1 votes
1 votes
1 answer
1
Bikram asked Aug 8, 2016
339 views
In the set of natural numbers the binary operators that are neither Associative nor Commutative areaddition subtraction multiplication ...
3 votes
3 votes
1 answer
2
Bikram asked Aug 8, 2016
466 views
A subset of a countable setis countable is finite may or may not be countable none of the options above are true
2 votes
2 votes
1 answer
3
Bikram asked Aug 8, 2016
553 views
Every element of some ring $(R,+,*)$ is such that $a*a=a.$ This ringis commutative is non-commutative may or may not be commutative none
2 votes
2 votes
2 answers
4
Bikram asked Aug 8, 2016
716 views
A group has 11 elements. The number of proper sub-groups it can have is0 11 5 4