Let mathrm{A}={1,2,3,4} and mathrm{R}={(1,2),(2,3),(1,4)} be a relation on mathrm{A} . Let mathrm{S}

English

Gujarati

Hindi

1.Relation and Function

easy

Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $A$ such that $\mathrm{R} \subset \mathrm{S}$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is...............

A

$16$

B

$15$

C

$14$

D

$13$

(JEE MAIN-2024)

Solution

All elements are included Answer is $16$

Standard 12

Mathematics

Share

Similar Questions

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

hard

Show that the relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R =\{(a, b):|a-b|$ is even $\},$ is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to each other and all the elements of $ \{2,4\}$ are

medium

Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation in $A$ given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is

easy

If $A = \left\{ {1,2,3,……m} \right\},$ then total number of reflexive relations that can be defined from $A \to A$ is

normal

If $R_{1}$ and $R_{2}$ are equivalence relations in a set $A$, show that $R_{1} \cap R_{2}$ is also an equivalence relation.

easy