The difference between ∈ and ⊂ I had a task where I had to figure if the argument was true or not.
$A=\{ n ∈ ℤ \mid n^2 < 5 \}, \quad  B=\{ 7, 8, \{2\}, \{2, 7, 8\}, \{\{7\}\} \}$
The first one was $\{-1, 2\} ∈ A$ and the answer to this was not true
 since the set is not an integer.
The second one was $\{-1, 2\} ⊂ A$ and the answer to this was true since
 -1 and 2 are elements of $A$.
I just can't seem to understand the difference between ∈ and ⊂ in this task and why the first argument was not true. Also it confuses me that the answer to the first one was that not true because the set is not an integer but aren't -1 and 2 integers?
There is other parts of this task that also add more confusion:

{2, 7, 8} ∈ B Answer: True since {2, 7, 8} is an element of set B
{2, 7, 8} ⊂ B Answer: Not true, for example 2 is not an element in set
  B


A set (e.g. $A$ or $B$) has individual elements. These elements are abstract objects (e.g., in $A$ they are integers), but sometimes confusingly these elements can be also sets ($B$ has elements that are integers as well as elements that are sets).
$\in$ means "is an [individual] element of." The elements of $A$ are integers $-2, -1, 0, 1, 2$, while the set $\{-1,2\}$ is not one of these integers.
The set $\{2,7,8\}$ is one of the elements of $B$, so $\{2,7,8\} \in B$.
$\subset$ means "is a subset of." The left-hand side of $\subset$ should be a set whose elements are also in the set on the right-hand side of $\subset$. The set $\{-1,2\}$ has two elements $-1$ and $2$, both of which are in $A$, so we write $\{-1,2\} \subset A$. The set $\{2,7,8\}$ has three elements $2,7,8$, but not all of them (actually none of them) are elements of $B$, so $\{2,7,8\} \not \subset B$.
