To prove set A = set B,

we first prove set A is a subset of set B,

and set B is a subet of set A

That means,

- all elements of set A are in set B
- all elements of set B are in set A

Since, both A and B have elements, they are equal

To write it in formula,

We first prove

A ⊂ B

& B ⊂ A

Then, A = B