Show that for all class $ \{A_i \}_{i\in I}$ of $A $, the relation $T$ is equivalence relation where $T$ is defined to be: $xTy$ iff exist $i\in I$ such that $\{ x,y\}\subseteq A_i$.
My attempt:
Reflexivity: $xTx$ because $A_i$ is a class of $A$, and $A_i$ is not empty.
Symmetry: If $xTy$, the there exist $i\in I$ such that $\{ x,y\}\subseteq A_i$. The same $i\in I$ is suitable to $yTx$. Transitivity: Let $xTy$ and $yTz$, so exist $i$ such that $\{ x,y\}\subseteq A_i$ and exist $j$ such that $\{ y,z\}\subseteq A_j$. Now clearly( I believe) $\{ x,z\}\subseteq A_i\Delta A_j$. Now what?
edit: all class $ \{A_i \}_{i\in I}$ of $A $ = All classes of $A$ under the relation $T$. Thank you.