Set Union Calculator: Find A ∪ B

What is a Set Union?

A set union is like mixing two groups of toys together! Imagine you have a box of red cars and a box of blue cars. When you put all these cars together in one big box, that's a union! We write it as A ∪ B, where A and B are our two sets.

How to Calculate a Set Union

To find the union of two sets, we gather all the unique items from both sets. It's like combining your toy collections with your friend's, but we only keep one of each toy, even if it appears in both collections.

Formula

We write the union of sets A and B like this:

\[ A \cup B = \{x : x \in A \text{ or } x \in B\} \]

This means:

• \(A\) and \(B\) are our two sets (like our two toy boxes)
• \(\cup\) means "union" (we're combining the sets)
• \(x\) is any item in either set
• \(\in\) means "is in" or "belongs to"

Calculation Steps

1. Write down all the items in Set A
2. Write down all the items in Set B
3. Make a new list with all items from A
4. Add any items from B that aren't already on the list
5. This new list is your union of A and B!

Example and Visual Representation

Let's use our toy car example:

Set A (red cars) = {Ferrari, Mustang}

Set B (blue cars) = {Mustang, Corvette}

To find A ∪ B, we list all unique cars:

A ∪ B = {Ferrari, Mustang, Corvette}

Let's show this with a picture:

In this picture, the red circle is Set A, the blue circle is Set B, and the whole colored area (red, blue, and the purple overlap) shows A ∪ B. It includes all cars from both sets, but we only list Mustang once even though it's in both sets!