If each element of the set \(X\) is also an element of the set \(Y\) and vice versa, then both are the same. In other words, a set is determined by its elements1, which is known as the extensionality principle.
\[\forall X~\forall Y (\forall z~(z\in X \Leftrightarrow z\in Y)\Rightarrow X=Y)\]
Please note that repeating the same elements in a set determines the same set. ↩