I stumbled upon a seemingly rudimentary proposition that I am having trouble writing out a proof for. The proposition goes something like,
Proposition: If $\{A_i|i\in I\}$ is a partition of $\mathcal A$, then there is an equivalence relation on $\mathcal A$ whose equivalence clases are precisely the sets $A_i, i \in I$.
Where $I$ is some indexing set.
How do I prove the statement ? I can't even decide on a good place to start.