Cardinality Calculator

Cardinality Calculator calculator can be used to determine the number of unique elements in sets and perform set operations like union, intersection, and difference.

Input Parameters

Calculation Results

Calculation Results

Enter values and click Calculate
Calculation Formula

N(A) = Count of unique elements in Set A

Cardinality Calculator Calculator Usage Guide

Learn how to use the Cardinality Calculator to analyze set operations and determine the number of unique elements in each set.

How to Use the Calculator

  1. Enter the elements of Set 1 in the first input field, separated by commas (e.g., 1,2,3,4,5)
  2. Enter the elements of Set 2 in the second input field, separated by commas (e.g., 3,4,5,6,7)
  3. Select the desired operation from the dropdown menu:
    • Cardinality (Set 1): Calculates the number of unique elements in Set 1
    • Cardinality (Set 2): Calculates the number of unique elements in Set 2
    • Union: Finds all unique elements that appear in either Set 1 or Set 2
    • Intersection: Finds all unique elements that appear in both Set 1 and Set 2
    • Difference (Set 1 - Set 2): Finds all unique elements that appear in Set 1 but not in Set 2
    • Symmetric Difference: Finds all unique elements that appear in either Set 1 or Set 2 but not in both
  4. Click the "Calculate" button to perform the calculation
  5. The results, including the calculation formula, will be displayed in the Results section

Understanding Set Operations

Set theory is a fundamental concept in mathematics and computer science. The operations available in this calculator include:

Cardinality

The cardinality of a set is simply the number of elements in the set. For example, if Set A = {1, 2, 3}, then the cardinality of Set A is 3.

Union

The union of two sets A and B (denoted as A ∪ B) contains all elements that are in A, in B, or in both. For example, if A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.

Intersection

The intersection of two sets A and B (denoted as A ∩ B) contains only the elements that are in both A and B. For example, if A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.

Difference

The difference of two sets A and B (denoted as A - B) contains all elements that are in A but not in B. For example, if A = {1, 2, 3} and B = {3, 4, 5}, then A - B = {1, 2}.

Symmetric Difference

The symmetric difference of two sets A and B (denoted as A Δ B) contains all elements that are in either A or B but not in both. For example, if A = {1, 2, 3} and B = {3, 4, 5}, then A Δ B = {1, 2, 4, 5}.