First slide

Introduction to Relations (XI) on Sets

Question

If a set $A$ has $n$ elements then the number of all relations on $A$ is

Moderate

A

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

$2^{n^{2}} - 1$
C

$2^{n^{}}$
D

none of these

Solution

$A x A$ has $n x n = n^{2}$ elements and any subset of $A x A$ is a relation on $A .$ The number of such subsets is $2^{n^{2}}$ .

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