The void relation on a set A is | vedclass

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

Question

(B) The void relation $R$ on a set $A$ is defined as $R = \emptyset \subseteq A 	imes A$. For a relation to be reflexive,$(a, a) \in R$ must hold for

Vedclass · Accepted Answer

Symmetric and transitive

Vedclass · Answer

(B) The void relation $R$ on a set $A$ is defined as $R = \emptyset \subseteq A 	imes A$. For a relation to be reflexive,$(a, a) \in R$ must hold for all $a \in A$. Since $R$ is empty,$(a, a) 
otin R$,so it is not reflexive. $A$ relation $R$ is symmetric if $(a, b) \in R \implies (b, a) \in R$. Since there are no elements in $R$,the condition is vacuously true. $A$ relation $R$ is transitive if $(a, b) \in R$ and $(b, c) \in R \implies (a, c) \in R$. Since there are no elements in $R$,the condition is vacuously true. Therefore,the void relation is symmetric and transitive.

The void relation on a set $A$ is

Similar Questions

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $A$ of human beings in a town at a particular time is given by:
$R = \{(x, y) : x \text{ and } y \text{ live in the same locality}\}$

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?
$(a, b) \in R, (b, c) \in R$ implies $(a, c) \in R$

Let $P$ be the relation defined on the set of all real numbers such that $P = \{(a,b) : \sec^2 a - \tan^2 b = 1\}$. Then $P$ is

The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is

Let $S$ be the set of all real numbers. Then the relation $R = \{(a, b) : 1 + ab > 0\}$ on $S$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module