Let n(A) = n . Then number of all relations on A is

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1.Relation and Function

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Let $n(A) = n$. Then the number of all relations on $A$ is

A

${2^n}$

B

${2^{(n)!}}$

C

${2^{{n^2}}}$

D

None of these

Solution

(c) Number of relations on the set $A = $Number of subsets of $A \times A = {2^{{n^2}}}$,

$[\because n(A \times A) = {n^2}]$

Standard 12

Mathematics

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