What is the Union and Intersection of Sets?
In set theory, the Union of two sets (A and B) represents a collection of all elements that belong to Set A, Set B, or both. Mathematically denoted as A ∪ B, it combines all unique members without duplication.
The Intersection of two sets (A and B) consists of elements that are common to both sets. If an element exists in A but not in B, it is excluded from the intersection. It is denoted by the symbol A ∩ B.
How to Use This Set Calculator
Using our tool is straightforward. Simply follow these steps:
- Enter the elements of Set A in the first text area, separated by commas.
- Enter the elements of Set B in the second text area.
- Click "Calculate Results" to generate the union, intersection, and relative difference.
- Review the Step-by-Step logic provided below each result to understand the underlying calculation.
Key Concepts in Set Operations
1. Disjoint Sets
If the intersection of two sets is empty (A ∩ B = Ø), they are called disjoint sets. This means they have no common elements.
2. Commutative Property
Both Union and Intersection follow the commutative law. This means A ∪ B is the same as B ∪ A, and A ∩ B is the same as B ∩ A.
3. Relative Difference
The difference (A - B) refers to elements that are in Set A but are NOT present in Set B. This is also known as the relative complement of B in A.
Frequently Asked Questions
Q: Does the order of elements matter?
A: No. In set theory, the order in which elements are listed does not change the set.
Q: Can sets contain duplicate values?
A: Standard sets only contain unique values. Our calculator automatically removes duplicates for you.
Q: What if one set is empty?
A: The union will be equal to the non-empty set, and the intersection will be an empty set.