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

English

Gujarati

Hindi

1.Relation and Function

normal

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

Share

Similar Questions

Let $N$ denote the set of all natural numbers and $R$ be the relation on $N \times N$ defined by $(a, b)$ $R$ $(c, d)$ if $ad(b + c) = bc(a + d),$ then $R$ is

hard

The relation $R =\{( x , y ): x , y \in z$ and $x + y$ is even $\}$ is :

medium

(JEE MAIN-2025)

Let $R$ be the relation on the set $R$ of all real numbers defined by $a \ R \ b$ if $|a – b| \le 1$. Then $R$ is

easy

If $A = \left\{ {1,2,3,……m} \right\},$ then total number of reflexive relations that can be defined from $A \to A$ is

normal

Show that each of the relation $R$ in the set $A =\{x \in Z : 0 \leq x \leq 12\},$ given by $R =\{(a, b):|a-b| $ is a multiple of $4\}$

medium