Let S be the set of all subsets of first 10 natural numbers. If a relation R is defined on set S such that (A, B)$\in$ R if    $A\cap B\ne \varphi ;whereA,B\in S$, then R is 

$\varphi \cap \varphi =\varphi \Rightarrow (\varphi ,\varphi )\notin R$

$\therefore$R is not reflexive 

Clearly R is symmetric but not transitive    $$\begin{gathered} ( if A =\{1,2,3\} , B=\{ 3, 4 \} , C = \{4,5,6\} then \\ A\cap B =\{3\} \ne \varnothing and B \cap C \ne \varnothing but A \cap C =\varnothing . \\ so not transitive ) \end{gathered}$$