Union - Definition, Examples, Quiz, FAQ, Trivia
Learn how to combine sets with simple explanations, colorful examples, and practice activities
What is Union of Sets?
The union of sets means combining all the elements from two or more sets together. Imagine you have two baskets of fruits:
• Basket A has an apple, banana, and orange
• Basket B has a banana, grape, and pear
The union of Basket A and Basket B would be all the fruits together: apple, banana, orange, grape, and pear. Notice we only list the banana once, even though it was in both baskets!
In math terms, the union of sets A and B contains all elements that are in A, or in B, or in both. We write this as A ∪ B (read as "A union B").
Key Concept
The union combines all elements from all sets, but never duplicates any element - each item appears only once in the union.
How to Find the Union of Sets
Finding the union of sets is like making a big list that includes everything from all the sets, but without repeating any items. Here's how to do it:
Step 1: Write down all the elements from the first set.
Step 2: Add all the elements from the second set that aren't already in your list.
Step 3: If you have more sets, keep adding their new elements.
Union Formula
This means the union of A and B is all x where x is in A or x is in B.
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
The union A ∪ B = {1, 2, 3, 4, 5, 6}
Notice we didn't write 3 and 4 twice, even though they appeared in both sets!
Remember
In a union, each element appears only once, no matter how many sets it was in originally.
The Union Symbol (∪)
Mathematicians use special symbols to make writing about sets quicker and clearer. The symbol for union is ∪, which looks like a wide letter "U".
How to use the union symbol:
• Write the first set
• Then write the ∪ symbol
• Then write the second set
For example: A ∪ B means "the union of set A and set B"
You can use the union symbol with more than two sets too:
A ∪ B ∪ C means "the union of sets A, B, and C"
The ∪ symbol helps us write about combining sets without needing lots of words. It's like a math shortcut!
Writing Tip
When writing by hand, make your ∪ symbol wide enough so it doesn't look like the letter U.
Union of Sets Examples
Let's look at some examples to understand union better:
Example 1: Favorite Colors
• Sarah's favorites: {red, blue, green}
• Tom's favorites: {blue, yellow, purple}
Their combined favorites: {red, blue, green, yellow, purple}
Example 2: Classroom Supplies
• Box A: {pencils, erasers, rulers}
• Box B: {markers, scissors, pencils}
Combined supplies: {pencils, erasers, rulers, markers, scissors}
Example 3: Numbers
• Set X: {1, 3, 5, 7}
• Set Y: {2, 4, 6, 8}
• Set Z: {5, 6, 7, 9}
X ∪ Y ∪ Z = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Example 4: Letters
• First letters: {a, b, c, d}
• Vowels: {a, e, i, o, u}
Combined letters: {a, b, c, d, e, i, o, u}
Notice how in each case, we combine all the items but never list anything twice!
Practice Tip
Try making your own sets with things around you (toys, books, snacks) and find their unions!
Union of Sets Quiz
Test your understanding with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about union of sets:
Math Trivia
Discover interesting facts about sets and unions:
Origin of Set Theory
Set theory was developed by Georg Cantor in the 1870s. He was studying mathematical infinity when he created this new way to think about collections of objects.
Universal Set
In math, we sometimes talk about a "universal set" that contains all possible elements we might consider. The union of any set with the universal set is always the universal set itself!
Computer Science
Unions are very important in computer programming. When you combine search results from different websites or merge contact lists on your phone, the computer is finding unions of sets!
Venn Diagrams
The circles we use to show unions and other set operations are called Venn diagrams, named after mathematician John Venn who popularized them in 1880.
