This calculator allows you to perform common operations on sets, such as union, intersection, difference, symmetric difference, and complement. Enter the elements of your sets, separated by commas, and select the desired operation.
Result:
function parseSetInput(inputString) {
if (!inputString) {
return [];
}
var elements = inputString.split(',').map(function(item) {
return item.trim();
}).filter(function(item) {
return item !== ";
});
// Use Set to ensure uniqueness, then convert back to array
return Array.from(new Set(elements)).sort();
}
function formatSetOutput(setArray) {
if (setArray.length === 0) {
return '{}';
}
return '{' + setArray.join(', ') + '}';
}
function calculateSetOperation() {
var setA = parseSetInput(document.getElementById('setAInput').value);
var setB = parseSetInput(document.getElementById('setBInput').value);
var universalSet = parseSetInput(document.getElementById('universalSetInput').value);
var selectedOperation = document.querySelector('input[name="setOperation"]:checked').value;
var result = [];
var errorMessage = ";
switch (selectedOperation) {
case 'union':
result = Array.from(new Set([…setA, …setB])).sort();
break;
case 'intersection':
result = setA.filter(function(element) {
return setB.includes(element);
}).sort();
break;
case 'differenceAB':
result = setA.filter(function(element) {
return !setB.includes(element);
}).sort();
break;
case 'differenceBA':
result = setB.filter(function(element) {
return !setA.includes(element);
}).sort();
break;
case 'symmetricDifference':
var diffAB = setA.filter(function(element) { return !setB.includes(element); });
var diffBA = setB.filter(function(element) { return !setA.includes(element); });
result = Array.from(new Set([…diffAB, …diffBA])).sort();
break;
case 'complementA':
if (universalSet.length === 0) {
errorMessage = 'Please provide a Universal Set for Complement of A operation.';
} else {
result = universalSet.filter(function(element) {
return !setA.includes(element);
}).sort();
}
break;
case 'complementB':
if (universalSet.length === 0) {
errorMessage = 'Please provide a Universal Set for Complement of B operation.';
} else {
result = universalSet.filter(function(element) {
return !setB.includes(element);
}).sort();
}
break;
default:
errorMessage = 'Invalid operation selected.';
}
var resultDisplay = document.getElementById('resultDisplay');
if (errorMessage) {
resultDisplay.innerHTML = 'Error: ' + errorMessage + ";
} else {
resultDisplay.innerHTML = " + formatSetOutput(result) + ";
}
}
.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
padding: 25px;
border-radius: 10px;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1);
max-width: 700px;
margin: 30px auto;
border: 1px solid #e0e0e0;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
font-size: 1.8em;
}
.calculator-container p {
margin-bottom: 15px;
line-height: 1.6;
color: #555;
}
.calc-input-group {
margin-bottom: 20px;
}
.calc-input-group label {
display: block;
margin-bottom: 8px;
color: #333;
font-weight: bold;
font-size: 1.05em;
}
.calc-input-group textarea {
width: calc(100% – 20px);
padding: 12px;
border: 1px solid #ccc;
border-radius: 6px;
font-size: 1em;
box-sizing: border-box;
resize: vertical;
min-height: 60px;
}
.radio-group {
margin-top: 10px;
padding: 10px;
background-color: #eef;
border-radius: 6px;
border: 1px solid #dde;
}
.radio-group input[type="radio"] {
margin-right: 8px;
transform: scale(1.1);
}
.radio-group label {
font-weight: normal;
color: #444;
margin-bottom: 5px;
display: inline-block;
font-size: 1em;
}
.calculate-button {
display: block;
width: 100%;
padding: 15px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 6px;
font-size: 1.1em;
font-weight: bold;
cursor: pointer;
transition: background-color 0.3s ease, transform 0.2s ease;
margin-top: 25px;
}
.calculate-button:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.calc-result {
margin-top: 30px;
padding: 20px;
background-color: #e9f7ef;
border: 1px solid #d4edda;
border-radius: 8px;
text-align: center;
box-shadow: inset 0 1px 3px rgba(0, 0, 0, 0.05);
}
.calc-result h3 {
color: #28a745;
margin-top: 0;
margin-bottom: 15px;
font-size: 1.5em;
}
.calc-result p {
font-size: 1.3em;
color: #333;
font-weight: bold;
word-wrap: break-word;
}
Understanding Set Notation and Operations
Set theory is a fundamental branch of mathematics that deals with collections of objects, known as sets. These objects are called elements or members of the set. Set notation provides a precise way to define and describe these collections and the relationships between them.
What is a Set?
A set is a well-defined collection of distinct objects. "Well-defined" means that there is a clear criterion for determining whether an object belongs to the set or not. "Distinct" means that each object in the set is unique; duplicates are not counted. Sets are typically denoted by capital letters (e.g., A, B, U), and their elements are enclosed in curly braces {}, separated by commas.
Examples:
Set of even numbers less than 10: E = {2, 4, 6, 8}
Set of primary colors: P = {Red, Yellow, Blue}
Set of vowels: V = {a, e, i, o, u}
The Universal Set (U)
The universal set, denoted by U, is the set of all possible elements under consideration in a particular context. All other sets in that context are subsets of the universal set. For example, if you're discussing numbers, the universal set might be all integers, all real numbers, or a specific range of numbers.
Common Set Operations
Set operations allow us to combine or compare sets to form new sets. This calculator supports the most common operations:
1. Union (A ∪ B)
The union of two sets A and B, denoted A ∪ B, is the set containing all elements that are in A, or in B, or in both. Duplicates are not listed.
Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.
2. Intersection (A ∩ B)
The intersection of two sets A and B, denoted A ∩ B, is the set containing all elements that are common to both A and B.
Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.
3. Difference (A – B or A \ B)
The difference of set A and set B, denoted A - B (or A \ B), is the set containing all elements that are in A but not in B.
Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A - B = {1, 2}. Conversely, B - A = {4, 5}.
4. Symmetric Difference (A Δ B)
The symmetric difference of two sets A and B, denoted A Δ B, is the set containing all elements that are in A or in B, but not in their intersection. It can be thought of as (A - B) ∪ (B - A).
Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A Δ B = {1, 2, 4, 5}.
5. Complement (A' or Ac)
The complement of a set A, denoted A' (or Ac), is the set of all elements in the universal set (U) that are not in A. This operation requires a defined universal set.
Example: If U = {1, 2, 3, 4, 5} and A = {1, 2, 3}, then A' = {4, 5}.
How to Use the Set Notation Calculator
Enter Set A Elements: In the first text area, type the elements of your first set, separated by commas (e.g., apple, banana, orange or 1, 5, 10, 15).
Enter Set B Elements: In the second text area, type the elements for your second set, also separated by commas.
Enter Universal Set Elements (Optional): If you plan to calculate the complement of a set, you must provide elements for the Universal Set in the third text area.
Select Operation: Choose the set operation you wish to perform using the radio buttons.
Calculate: Click the "Calculate Set Operation" button.
View Result: The result will be displayed in standard set notation (e.g., {element1, element2}) in the "Result" section.
This calculator simplifies complex set operations, making it easier to understand and verify results for various mathematical and logical problems.