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