A={1},no of transitive relations are 2.

A={1,2},no of transitive relations are 13.

A={1,2,3},no of transitive relations are 171.

A={1,2,3,4},no of transitive relations are 3994.

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Sanjay Sharma
asked
in Set Theory & Algebra
Mar 7, 2017

30,703 views
5 votes

1

9 votes

Best answer

https://en.wikipedia.org/wiki/Transitive_relation#Counting_transitive_relations

https://www.quora.com/How-do-I-find-number-of-transitive-relations-on-a-set

On the basis of given link,

There is No general formula to counts the number of transitive relations on a finite set.

a) n=1, number of transitive relations will be 2

b) n=2, number of transitive relations will be 13

There are direct formulas to count other types of relations.

No. of relations =2

^{mn}No. of reflexive relations =2

^{n(n-1)}No. of irreflexive relations = 2

^{n(n-1)}No. of symmetric relations = 2

^{n(n+1)/2}No. of asymmetric relations = 3

^{n(n-1)/2}No. of Anti Symmetric Relations = 2

^{n}* 3^{n(n-1)/2}

I hope te answer is helpful :)

4

0 votes

https://cs.uwaterloo.ca/journals/JIS/VOL7/Pfeiffer/pfeiffer6.pdf Please refer to this paper. first take 2 elements (pair) at a time and then take 3 elements ata time in sequence to form transitive relation.