Property of Set Operations
Set operations have several important properties that govern their behavior. Here are some fundamental properties of set operations:
Closure Property
- Set operations are closed under their respective operations, meaning that performing an operation on sets results in another set.
- For example, the union, intersection, and difference of sets always produce sets as their results.
Commutative Property
- Union: A ∪ B = B ∪ A
- Intersection: A ∩ B = B ∩ A
- Symmetric Difference: A Δ B = B Δ A
Associative Property
- Union: (A ∪ B) ∪ C = A ∪ (B ∪ C)
- Intersection: (A ∩ B) ∩ C = A ∩ (B ∩ C)
Distributive Property
- Union over Intersection: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
- Intersection over Union: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Identity Property
- Union: A ∪ ∅ = A
- Intersection: A ∩ U = A, where U represents the universal set
- Symmetric Difference: A Δ ∅ = A
Complement Property
- Union: A ∪ A’ = U, where U is the universal set
- Intersection: A ∩ A’ = ∅ (the empty set)
Absorption Property
- Union over Intersection: A ∪ (A ∩ B) = A
- Intersection over Union: A ∩ (A ∪ B) = A
Related Article
Set Operations
Sets are collections of unique objects or elements, and set operations are mathematical operations carried out on sets.
Table of Content
- What is Set Operation
- Union
- Intersection
- Disjoint
- Set Difference
- Complement
- Addition & Subtraction
- Property of Set Operations
- Conclusion of Set Operation
- Set Operations – FAQs