Let a set $A = A _ { 1 } \cup A _ { 2 } \cup \ldots \cup A _ { k }$, where $A _ { i } \cap A _ { j } = \phi$ for $i \neq j ; 1 \leq i , j \leq k$. Define the relation $R$ from $A$ to $A$ by $R = \left\{ ( x , y ) : y \in A _ { i } \right.$ if and only if $\left. x \in A _ { i } , 1 \leq i \leq k \right\}$. Then, $R$ is:\\
(1) reflexive, symmetric but not transitive\\
(2) reflexive, transitive but not symmetric\\
(3) reflexive but not symmetric and transitive\\
(4) an equivalence relation