# Intersection and union of 2 sets

##### Intros

###### Lessons

##### Examples

###### Lessons

**Finding the Intersection & Union of 2 Sets**You are given the following Venn diagram:

- Consider the following:
- Universal Set $U =$ {1, 2, 3, 4, 5, 6, 7, 8}

- Set A = {1,2,3,4,5,6}

- Set B = {2,4,6,8}

- Consider the following:
- A = {$m | m = 4x, 0 \leq x \leq 3, x \in I$}

- B = {$n | n = 2x, 0 \leq x \leq 6, x \in I$}

**Using the Principle of Inclusion and Exclusion**Kevin asked 50 people if they liked to play soccer or basketball. 10 people didn't like either of them. 25 people liked soccer. 30 people liked basketball. How many people liked both soccer and basketball?

- Willy surveyed 30 people at a restaurant to see if they ordered noodles or rice. 10 people ordered both rice and noodles. 5 people only ordered a drink. 3 people ordered only rice.

###### Free to Join!

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

In this section we will learn about intersection and union of 2 sets.

Let A and B be sets. Then, the definitions for intersection and union is the following:

** Intersection**: A set of elements where the elements show up both in A and B. We call this intersection A$\cap$B. Sometimes people refer to the symbol $\cap$ as the word "and".

__ Union__: A set of all elements that appears in A, in B, or both in A and B. We call this union A$\cup$B. Sometimes people refer to the symbol $\cup$ as the word "or".

Here is a definition that may be useful:

A\B: The set of elements that is in A but **not** in B. In short, it is just A minus B.

The principle of inclusion and exclusion of 2 sets says the following:

remaining today

remaining today