# belong to and subset in the set

My question is I can't understand the difference between belong and subset.

Set theory: difference between belong/contained and includes/subset?

I've read this already but I didn't get it yet...

I hope you tell me how did they answer this question in this way, I am really confused. Why they didn't put belong to?? And why belong to is wrong??

I don't know where should I put subset or belong to...thank you.

• There's a mistake in your example. $2\in \{2,4,6,8\}$ simply because $2$ is one of the elements of $\{2,4,6,8\}$. – Kevin Arlin Sep 29 '14 at 17:22

I find something confusing in Ex. 13. In particular, the sentence "$2$ is a set, which contains one elements?".
If you consider $2,4,6,8$ as integer numbers then $\{2,4,6,8\}$ is a set that contains four elements: $2,4,6$ and $8.$
Since $2$ is an element of such a set you can say that $2$ belongs to it: $2\in \{2,4,6,8\}.$ Now, $\{2\}$ is a set that contains one element: $2.$ So, you can say that $\{2\}$ is contained in the given set $\{2\}\subset \{2,4,6,8\}.$ (In fact, they are equivalent.) But note that $\{2\}$ is not an element of the bigger set: the elements are $2,4,6$ and $8,$ not a set containing $2.$ So, it is $\{2\}\notin\{2,4,6,8\}.$
Belonging to a set is a concept applied only to an element of a set, take heed that $2$ is an element and $\{2\}$ is a set (containing $2$), since a set is a collection of elements it is not true that $\{2\}\in\{2,4,6,8\}$, but it is true that $2\in\{2,4,6,8\}$