A subset is a set contained within another set. If set A = {1, 2} and set B = {1, 2, 3, 4}, then A is a subset of B. Every set is a subset of itself. The empty set is a subset of every set.

A proper subset is a subset that is not equal to the original set. A has 2 elements; B has 4. Since A ≠ B, A is a proper subset of B. The number of subsets of a set with n elements is 2^n.

Subsets appear in set theory, logic, and computer science. In probability, events are subsets of the sample space. In databases, queries select subsets of records. The concept is simple but foundational to modern mathematics.

• Set contained within another set
• Every set is a subset of itself
• Empty set is a subset of every set
• Number of subsets is 2^n