The number of reflexive relations on a set wi | vedclass

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

Question

(D) relation $R$ on a set $A$ with $n$ elements is reflexive if $(a, a) \in R$ for every $a \in A$.There are $n^2$ total possible ordered pairs in the

Vedclass · Accepted Answer

$2^{12}$

Vedclass · Answer

(D) relation $R$ on a set $A$ with $n$ elements is reflexive if $(a, a) \in R$ for every $a \in A$.There are $n^2$ total possible ordered pairs in the Cartesian product $A 	imes A$.For a relation to be reflexive,all $n$ elements of the form $(a, a)$ must be present in the relation.The remaining $n^2 - n$ ordered pairs can either be in the relation or not,giving $2^{n^2 - n}$ possibilities.For a set with $n = 4$ elements,the number of reflexive relations is $2^{4^2 - 4} = 2^{16 - 4} = 2^{12}$.

The number of reflexive relations on a set with $4$ elements is equal to

Similar Questions

Let $I$ be the set of positive integers. $R$ is a relation on the set $I$ given by $R = \{(a, b) \in I \times I \mid \log_2(a/b) \text{ is a non-negative integer} \}$. Then $R$ is:

Let $r$ be a relation from $R$ (set of real numbers) to $R$ defined by $r = \{(a,b) \mid a,b \in R \text{ and } a - b + \sqrt{3} \text{ is an irrational number} \}$. The relation $r$ is

Let the relation $R$ on the set $M = \{1, 2, 3, \dots, 16\}$ be given by $R = \{(x, y) : 4y = 5x - 3, x, y \in M\}$. Then the minimum number of elements required to be added in $R$, in order to make the relation symmetric, is equal to

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false?

For real numbers $x$ and $y$,let $xRy$ if and only if $x - y + \sqrt{2}$ is an irrational number. Then $R$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module