Let X be a family of sets and R be a relation | vedclass

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

Question

(B) relation $R$ is defined on a family of sets $X$ such that $A R B$ if $A \cap B = \emptyset$. $1$. Reflexive: For $R$ to be reflexive,$A R A$ must

Vedclass · Accepted Answer

Symmetric

Vedclass · Answer

(B) relation $R$ is defined on a family of sets $X$ such that $A R B$ if $A \cap B = \emptyset$. $1$. Reflexive: For $R$ to be reflexive,$A R A$ must hold for all $A \in X$,which means $A \cap A = \emptyset$. This is only true if $A = \emptyset$. Since it does not hold for all $A \in X$,$R$ is not reflexive. $2$. Symmetric: If $A R B$,then $A \cap B = \emptyset$. Since intersection is commutative,$B \cap A = \emptyset$,which implies $B R A$. Thus,$R$ is symmetric. $3$. Transitive: If $A R B$ and $B R C$,then $A \cap B = \emptyset$ and $B \cap C = \emptyset$. This does not necessarily imply $A \cap C = \emptyset$. For example,let $A = \{1\}$,$B = \{2\}$,and $C = \{1\}$. Here $A \cap B = \emptyset$ and $B \cap C = \emptyset$,but $A \cap C = \{1\} 
eq \emptyset$. Thus,$R$ is not transitive. Therefore,the relation is symmetric.

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by '$A$ is disjoint from $B$'. Then $R$ is

Similar Questions

Let $R$ be an equivalence relation defined on a set containing $6$ elements. The minimum number of ordered pairs that $R$ should contain is

In $\mathbb{R}$, a relation $p$ is defined as follows: $\forall a, b \in \mathbb{R}$, $a \ p \ b$ holds if $a^2-4ab+3b^2=0$. Then:

Let $X$ be a non-void set. If $\rho_1$ and $\rho_2$ are transitive relations on $X$, then which of the following is true?

$A$ relation $R$ is defined on the set of natural numbers such that $m$ is related to $n$ if $m$ is a multiple of $n$. Then the relation is:

In the set of all $3 \times 3$ real matrices, a relation is defined as follows: $A$ matrix $A$ is related to a matrix $B$ if and only if there exists a non-singular $3 \times 3$ matrix $P$ such that $B = P^{-1} A P$. This relation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module