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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)
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+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)


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