Difficulty understanding notations for equivalence classes

Question

So, this is the question I need to answer, and I am having trouble understanding the notations used, especially this line:

[a]i denotes the equivalence class of a under Ri(i = 1,2)

Given an equivalence relation (in terms of ordered pairs), I know how to find the equivalence classes. But I am unable to understand how to obtain the equivalence relation here, and what I am supposed to do after that.

Here is the entire question:

A is a set, and R1,R2 ⊆ A x A are equivalence relations on A. For a ∈ A, [a]i denotes the equivalence class of 'a' under Ri(i = 1,2) and [a] denotes the equivalence class of 'a' under R1 ∩ R2. Define [a] in terms of [a]1 and [a]2

Answer 1

I guess since you are new to this topic, maybe the intuition isn't there yet. Here is a simple example that you can try, and hopefully it helps you get the answer.

Let $A$ be the set of integers. Let $R_1$ be the equivalence relation of 'congruent modulo 2'. We denote the equivalence classes by $[n]_2$. What is the set represented by $[0]_2$?

$[0]_2 = $ the even numbers $ = \{ -2, 0, 2, 4, 6, \dots \}$.

Let $R_2$ be the equivalence relation of 'congruent modulo 3'. We denote the equivalence classes by $[n]_3$. What is the set represented by $[0]_3$?

$[0]_3 = $ the multiples of $3$ $ = \{ -3, 0, 3, 6, \dots \}$.

What is the equivalence relation defined by $R_3 = R_1 \cap R_2$?

It is the equivalence relation of 'congruent modulo 6'.

Denote this equivalence relation by $[n]_6$. What is the set represented by $[0]_6$?

$[0]_6 = $ the multiples of $6$ $ = \{ -6, 0, 6, 12, \dots \}$.

Now, what is the relation between $[0]_2$, $[0]_3$, and $[0]_6$?

$[0]_6 = [0]_2 \cap [0]_3$

From this answer, you can guess the answer to your original question. Now try to turn it into a proof!