QJEEM24Madd34: JEE Main 2024 Mathematics - Class 11 JEEM24Madd34 Solution: Let . Suppose is the set of all the subsets of , then the…

Let $S=\{1,2,3, \ldots, 10\}$

$R=\{(A, B): A \cap B \neq \phi ; A, B \in M\}$

For Reflexive,

$M$ is subset of ' $S$ '

So $\phi \in \mathrm{M}$

for $\phi \cap \phi=\phi$

$\Rightarrow$ but relation is $\mathrm{A} \cap \mathrm{B} \neq \phi$

So it is not reflexive.

For symmetric,

$\begin{array}{ll}\text { ARB } & \mathrm{A} \cap \mathrm{B} \neq \phi, \\\Rightarrow \mathrm{BRA} & \Rightarrow \mathrm{B} \cap \mathrm{A} \neq \phi,\end{array}$

So it is symmetric.

For transitive,

$\begin{aligned}\text { If } A & =\{(1,2),(2,3)\} \\B & =\{(2,3),(3,4)\} \\C & =\{(3,4),(5,6)\}\end{aligned}$

$\mathrm{ARB}$ & $\mathrm{BRC}$ but $\mathrm{A}$ does not relate to $\mathrm{C}$ So it not transitive