So this is a problem for one of my classes. I don't even know where to start...thanks for any help!

Let A be a non-empty set, and let E1 and E2 be equivalence relations on A with associated partitions D1 and D2 , respectively. Let E be the equivalence relation on A defined by E = E1 ∩ E2 , and D its associated partition. Come up with a proposition describing the relationship between

D1 , D2 and D. Prove your result.