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,

$\mathrm{ARB}$

$\mathrm{A} \cap \mathrm{B} \neq \phi,$

$\Rightarrow \mathrm{BRA} \quad \Rightarrow \mathrm{B} \cap \mathrm{A} \neq \phi$,

So it is symmetric.

For transitive,

If $\mathrm{A}=\{(1,2),(2,3)\}$

$ B=\{(2,3),(3,4)\} $

$C=\{(3,4),(5,6)\}$

$ARB$ $BRC$ but $A$ does not relate to $C$

So it not transitive