Given $X$ a non-empty set and $\mathcal{P}(X)$ with relation $\sim$ on $\mathcal{P}(X)$: $$\forall A, B \subset X: A \sim B \Leftrightarrow A \Delta B \text{ is finite}$$
Prove that $\sim$ is an equivalence relation on $\mathcal{P}(X)$.
I know that I have to prove that the relation is reflexive, symmetric and transitive. But I have no idea on how to start.
Just apply the definition. For reflexive, is $A \Delta A$ finite? For symmetric, does $A \Delta B \text{ finite} \implies B\Delta A \text { finite}?$ The purpose of questions like this is to make sure you understand the definition.