First slide

Introduction to Relations (XI) on Sets

Question

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

Easy

A

$2^{n}$
B

$2^{(n)!}$
C

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

None of these

Solution

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

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