Set Theory Calculator
Set Operations
Compute union, intersection, and difference of two sets (enter comma-separated numbers)
Subset & Power Set
Check subset relationships and compute power set size
Formula
A ∪ B = {x : x ∈ A or x ∈ B} | A ∩ B = {x : x ∈ A and x ∈ B} | A \ B = {x : x ∈ A and x ∉ B} | |P(A)| = 2^|A|
Frequently Asked Questions
What is the difference between union and intersection?
Union (A ∪ B) combines all elements from both sets. Intersection (A ∩ B) includes only elements that appear in both sets. For A = {1,2,3} and B = {2,3,4}: union = {1,2,3,4}, intersection = {2,3}.
What is symmetric difference?
The symmetric difference (A △ B) contains elements that are in either A or B but not in both. It equals (A \ B) ∪ (B \ A). For A = {1,2,3} and B = {2,3,4}: A △ B = {1,4}.
What is a power set?
The power set P(A) is the set of all subsets of A, including the empty set and A itself. If |A| = n, then |P(A)| = 2^n. For A = {1,2}, P(A) = {∅, {1}, {2}, {1,2}}, so |P(A)| = 4.