Subsets
Recall that a set is a collection of elements.
A set A is a subset of a set B if every element in A is also in B.
For example, if A = {1, 3, 5} and B = {1, 2, 3, 4, 5}, then A is a subset of B, and we write
The line under the sideways U means that A may also be equal to B (that is, they may be identical sets). If we want to say that A is a proper subset of B (that means: it's a subset, but there is at least one element in B that is not in A) 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 U:
