Embibe Experts Solutions for Chapter: Set Theory and Relations, Exercise 1: WBJEE 2019

If the total number of $m$-element subsets of the set $A=\left\{a_1,a_2,\dots ,a_n\right\}$ is $k$ times the number of $m$ element subsets containing $a_4$, then $n$ is

Let the relation $\rho$ be defined on $R$ by $a\rho b$ holds if and only if $a-b$ is zero or irrational, then

Let ${\rho }_1$ and ${\rho }_2$ be two equivalence relations defined on a non-void set $S$. Then

Let the relation $\rho$ be defined on $R$ as $a\rho b$ if $1+ab>0.$ Then

On $R$, a relation $\rho$ is defined by $x\rho y$ if and only if $x-y$ is zero or irrational. Then,

On the set $R$ of real numbers, the relation $\rho$ is defined by $x\rho y,(x,y)\in R$

Let $\rho$ be a relation defined on $N,$ the set of natural numbers, as $\rho =\left\{\right(x,y)\in N\times N:2x+y=41\}.$ Then