This tool helps you easily calculate the union, intersection, difference, and complement of sets.
How to Use the Set Calculator
To use the Set Calculator, input your two sets in the provided fields. Sets should be entered as comma-separated values. Then, select the operation you want to perform: Union, Intersection, or Difference. Click the “Calculate” button to see the result displayed in the “Result” field.
How It Calculates the Results
The Set Calculator performs the following operations:
- Union: Combines all unique elements from both sets.
- Intersection: Finds the common elements shared by both sets.
- Difference: Finds elements in the first set that are not present in the second set.
Limitations
The Set Calculator has the following limitations:
- Input must be valid, comma-separated values. Whitespace around values will be ignored.
- Duplicate elements in the input will be treated as a single element.
- The calculator only supports basic set operations.
Use Cases for This Calculator
Calculating Union of Two Sets
Enter the elements of the two sets separated by commas and get the union set as the result. The calculator will remove duplicate elements and display a new set containing all unique elements from the two sets combined.
Calculating Intersection of Two Sets
Input the elements of both sets and receive the intersection set as the output. You will see a set that contains only the elements that are common to both input sets.
Finding the Relative Complement of Two Sets
Type in the elements of two sets to find the relative complement, also known as the difference set. The calculator will display all elements that exist in the first set but not in the second set.
Finding the Symmetric Difference of Two Sets
Provide the elements of the two sets to compute the symmetric difference set. You will receive a new set with elements that are in either of the input sets but not in their intersection.
Determining if Two Sets Are Equal
Input the elements of two sets to check if they are equal. You will receive a confirmation indicating whether the two sets are identical or not based on their elements.
Checking if a Set is a Subset of Another
Enter the elements of two sets to determine if the first set is a subset of the second set. The calculator will analyze the sets and provide you with the result indicating if the first set is contained within the second set.
Finding the Cartesian Product of Two Sets
Input the elements of two sets to calculate their Cartesian product. You will see a new set containing all possible ordered pairs where the first element comes from the first set and the second element from the second set.
Calculating the Power Set of a Set
Enter the elements of a set to find its power set, which includes all possible subsets of the given set. The calculator will generate a list of subsets that can be formed from the input set.
Calculating the Cardinality of a Set
Input the elements of a set to determine its cardinality, which is the count of elements in the set. You will receive the total number of elements in the set as the output.
Performing Set Operations with Multiple Sets
Input elements of multiple sets along with the operation you want to perform (like union, intersection, etc.) to perform operations involving more than two sets. You will get the resulting set based on the specified operation and input sets.