I am confused with braces inside braces. Please help me to figure out which are elements and which are sets in this set given in the picture .

Question

Does 2 belongs to this set A? Does 2 an element of A..? (https://i.stack.imgur.com/Plc8B.jpg)

Answer 1

$A = \{1, \{2,3\}, \{4\}\}$

i) Is $2 \in A$. or Is $2$ an element of $A$?

Well.... What are the elements of $A$? The elements of $A$ are: a)$1$,b)$\{2,3\}$ and c) $\{4\}$. Are any of those three elements equal to $2$? No. None of them are equal to $2$. So $2 \not \in A$.

ii) Is $\{2\}\in A$. or Is $\{2\}$ an element of $A$?

Well.... What are the elements of $A$? The elements of $A$ are: a)$1$,b)$\{2,3\}$ and c) $\{4\}$. Are any of those three elements equal to $\{2\}$? No. None of them are equal to $\{2\}$. So $\{2\} \not \in A$.

Answer 2

The answer to both questions is no.

$2$ is not an element of $A$ and { 2} is not an element of A either.

A has three elements, namely $1$, {2,3}, and {4} and none of the above is among them.

Answer 3

Remove the outermost brackets. What's left is your elements, separted by commas. So here neither $2$ nor $\{2\}$ are elements.