Let X be a family of sets and R be a relation on X defined by ‘A is disjoint from B’ . T

English

Gujarati

Hindi

1.Relation and Function

medium

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

A

Reflexive

B

Symmetric

C

Anti-symmetric

D

Transitive

Solution

(b) Clearly, the relation is symmetric but it is neither reflexive nor transitive.

Standard 12

Mathematics

Share

Similar Questions

The minimum number of elements that must be added to the relation $R =\{( a , b ),( b , c )\}$ on the set $\{a, b, c\}$ so that it becomes symmetric and transitive is:

hard

(JEE MAIN-2023)

A relation on the set $A\, = \,\{ x\,:\,\left| x \right|\, < \,3,\,x\, \in Z\} ,$ where $Z$ is the set of integers is defined by $R= \{(x, y) : y = \left| x \right|, x \ne – 1\}$. Then the number of elements in the power set of $R$ is

hard

(JEE MAIN-2014)

Let $A$ be the set of all functions $f: Z \rightarrow Z$ and $R$ be a relation on $A$ such that $R =\{( f , g ): f(0)= g (1)$ and $f(1)= g (0)\}$. Then $R$ is:

medium

(JEE MAIN-2025)

Check whether the relation $R$ in $R$ defined by $S =\left\{(a, b): a \leq b^{3}\right\}$ is reflexive, symmetric or transitive.

medium

The relation $R= \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is

medium