Subset Calculator

Determine subset, superset, and proper subset relationships between two sets. Find intersection and union.

Enter Two Sets

Result

Relationship
--
A is subset of B (A \u2286 B)--
A is proper subset of B (A \u2282 B)--
B is subset of A (B \u2286 A)--
A equals B (A = B)--
Intersection (A \u2229 B)--
Union (A \u222A B)--
A \\ B (Difference)--
B \\ A (Difference)--
|A|--
|B|--

Step-by-Step Analysis

Understanding Subsets

In set theory, a set A is a subset of set B if every element of A is also an element of B. This fundamental concept is central to discrete mathematics, logic, and computer science.

Set Relationships

Subset (\u2286)

A \u2286 B means every element in A is also in B. A can equal B.

{1,2} \u2286 {1,2,3} is TRUE

Proper Subset (\u2282)

A \u2282 B means A \u2286 B and A \u2260 B (B has at least one extra element).

{1,2} \u2282 {1,2,3} is TRUE

Superset (\u2287)

B \u2287 A means B contains all elements of A. Reverse of subset.

{1,2,3} \u2287 {1,2} is TRUE

Set Operations

  • Intersection (A \u2229 B): Elements common to both A and B.
  • Union (A \u222A B): All elements in A or B or both.
  • Difference (A \\ B): Elements in A but not in B.
  • Symmetric Difference (A \u2206 B): Elements in A or B but not both.

Properties of Subsets

  • The empty set \u2205 is a subset of every set.
  • Every set is a subset of itself (A \u2286 A).
  • If A \u2286 B and B \u2286 A, then A = B.
  • If A \u2286 B and B \u2286 C, then A \u2286 C (transitivity).