First slide

Introduction to Relations (XI) on Sets

Question

If A is a finite set having n elements,then the number of relations which can be defined in A is

Easy

A

$2^{n}$
B

$n^{2}$
C

₂ $n^{2}$
D

nⁿ

Solution

n(A)=n
$\Rightarrow n (A \times A) = n \times n = n^{2}$
$n [P (A \times A)] = 2^{n^{2}}$
Number of relations in A= $2^{n^{2}}$

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