Equivalence relation - Equilavence classes explanation

Question

I have the following equivalence relation problem.

$Let \ R\subseteq 2^S*2^S = \{(A,B):|A\cap T|=|B \cap T|\}\ where\ S=\{0,1,2\} \ and \ T=\{1,2\} \ Show \ that \ R \ is \ a \ equivalence \ relation \ to \ 2^S \ and \ describe \ the \ equivalence \ classes\ $

I understand that in order to show that $R$ is an equivalence relation I need to show that is $R$ is symmetric, reflexive and transitive.

Though I have two questions.

1. What the result of $2^S$ will be?
2. What steps do I need to follow to find the equivalence classes of an equivalence relation?

Answer 1

I already gave you an example in the comment. For another one:

$$|\{1\}\cap T|=1\implies X\in\left[\,\{1\}\,\right]\iff |X\cap T|=1$$

so for example, we have in this case

$$\{1\}\,,\,\{0\}\,,\,\{0,2\}\,,\,\{1,2\}\in\left[\,\{1\}\,\right]$$

Now you try other cases.