Set Theory Calculator
This Set Theory Calculator is designed for students and professionals to easily perform set operations, including union, intersection, and complement. Solve complex set-related problems with ease and accuracy.
Calculator
Results
Authoritative Content
Data Source and Methodology
All calculations are based on standard set theory operations as outlined in mathematics literature. Learn more. All calculations are strictly based on the formulas and data provided by this source.
The Formula Explained
Union: \( A \cup B = \{x | x \in A \lor x \in B\} \)
Intersection: \( A \cap B = \{x | x \in A \land x \in B\} \)
Difference: \( A - B = \{x | x \in A \land x \notin B\} \)
Glossary of Terms
- Union (A ∪ B): The set containing all elements from both sets A and B.
- Intersection (A ∩ B): The set containing elements common to both sets A and B.
- Difference (A - B): The set containing elements in set A but not in set B.
How It Works: A Step-by-Step Example
Example: Given Set A = {1, 2, 3} and Set B = {3, 4, 5}, the union is {1, 2, 3, 4, 5}, intersection is {3}, and difference is {1, 2}.
Frequently Asked Questions (FAQ)
What is set theory?
Set theory is a branch of mathematical logic that studies sets, which are collections of objects.
How do I input sets?
Enter each element separated by a comma, without spaces (e.g., "1,2,3").
Can sets contain different types of elements?
In mathematical set theory, sets are typically composed of similar elements, but this tool accepts numbers for simplicity.
What are some applications of set theory?
Set theory is used in various fields including computer science, logic, statistics, and many areas of mathematics.
How are the results calculated?
The calculator uses basic set operations defined in mathematics to compute the results.