Recall that a set is a collection of elements.
A set is a subset of a set if every element in is also in .
For example, if and , then is a subset of , and we write
The line under the sideways means that may also be equal to (that is, they may be identical sets). If we want to say that is a proper subset of (that means: it's a subset, but there is at least one element in that is not in ) then we can remove the line:
To write that a set is not a subset of another set, just put a slash through the sideways :