Let n(A) = n. Then the number of all relation | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The set $A$ has $n$ elements,so $n(A) = n$. The Cartesian product $A 	imes A$ contains $n 	imes n = n^2$ elements. $A$ relation on set $A$ is de

Vedclass · Accepted Answer

$2^{n^2}$

Vedclass · Answer

(C) The set $A$ has $n$ elements,so $n(A) = n$. The Cartesian product $A 	imes A$ contains $n 	imes n = n^2$ elements. $A$ relation on set $A$ is defined as any subset of $A 	imes A$. The total number of subsets of a set with $m$ elements is $2^m$. Since $A 	imes A$ has $n^2$ elements,the total number of subsets of $A 	imes A$ is $2^{n^2}$. Therefore,the number of all relations on $A$ is $2^{n^2}$. Thus,the correct option is $C$.

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

Similar Questions

If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$,then the number of relations from $A$ to $B$ is

Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : y = x + 1\}$. Write down the domain,codomain,and range of $R$.

The figure shows a relation between the sets $P$ and $Q$. Write this relation in roster form. What is its domain and range?

Two finite sets $A$ and $B$ are such that $n(A) = 2$ and $n(B) = 3$. Then the total number of relations from $A$ to $B$ is:

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, b) \in R$ implies $(b, a) \in R$

Vedclass Test Series

Exam Paper Generator

Online Exam Module