The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
+1 vote
How many binary relations are there on a set $A$ with $n$ elements?
asked in Set Theory & Algebra by Veteran (42.4k points) | 263 views

2 Answers

+9 votes
Best answer

Total number of  binary relation from n element set to itself is $2^{n^{2}}$ I.e.n2 entries with two choice take it or not.

answered by Veteran (55.4k points)
selected by
+1 vote

∣A∣ =n

∣A⨉A∣ = n^2

Relation is the subsets of A⨉A, so the total no of binary relation on set A = cardinality of power set of (A⨉A)  = ∣ p(A⨉A) ∣ =2^(n^2)


So, the correct answer is 2^(n^2).


answered by Veteran (12.7k points)

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

28,947 questions
36,793 answers
34,690 users