If every element in Set A is also in Set B, then Set A is a subset of Set B.
Proper subset
If S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is therefore a proper subset of any nonempty set.
For example, consider a set {1,2,3,4,5}. Then {1,2,4} and {1} are proper subsets, while {1,2,6} and {1,2,3,4,5} are not.