In this lesson, learn about how you use sets and their unions in everyday life.

Learn how to appropriately write them so that you can communicate with others about sets. Also, learn how easy they are to use.

## What Is a Set?

A **set** is a group of items. They can be related items or a random selection of different items.

A set just tells you that you have grouped them together or that you have put them together in the same bag.If you had a grouping of tools, such as a hammer, screwdriver, and pliers, you would say that you have a set consisting of a hammer, screwdriver, and pliers. If you had a random grouping such as a cell phone, a pencil, and a marble, you would say you had a set consisting of a cell phone, a pencil, and a marble.In math, sets usually consist of numbers instead of objects. But once you get into applying sets, you can use them to organize any collection of items or numbers.

## What Is the Union of Sets?

The **union of sets**, then, is the combination of two or more sets.

Just like when you unite two people or when you unite two pools of cash, what was separate before is now all together. What wasn’t shared before is now shared. What one had now belongs to both.Say we united our tools set and our random set from before.

Our union of sets now consists of a hammer, screwdriver, pliers, cell phone, pencil, and marble.What if our random set also included a hammer? Does that mean our union of sets also has two hammers? For sets, the number of items is not important, only what is contained. So, no duplicates are written in the set. We are only concerned about what is in the set.

If we had four flowers, the set would still say ‘flower’ and not ‘flower four times.’ The order you write things in doesn’t matter as long as you list everything you have.

## Symbols Used

**Set notation** refers to the specific symbols used to tell people you are talking about sets of things.

Sets are written with curly brackets and commas separating each item in the set.

The above are two examples of sets.

The first lists objects and the second uses numbers. You can substitute numbers or symbols for your objects if you wanted to write it in a shorter manner.To denote the union of sets, a symbol that looks like the letter u is used. You can write out both sets, or you can label each set with a name and write it with the names instead.

Because we have labeled our sets with the letter, we don’t need to use the curly brackets with those letters.

Either way of writing the union of sets is acceptable. Usually, though, naming your sets and using their names makes for a much cleaner problem. If you have several lines of work, it’s much easier and quicker to write the names instead of all the items all the time, especially if the sets are large.

## Real-World Usefulness

Learning about sets and their unions is useful because we see sets all around us every day. Most people have a set of kitchen appliances, a set of utensils, and a set of serving dishes, etc.

All the sets belonging to the kitchen, when united, make a larger set including all the items needed to fill a kitchen. When cooking, you have a set of dry ingredients and wet ingredients that when united make a whole dish. So, we use sets in our everyday life and we create unions of sets all the time. Being able to write it mathematically allows us to communicate our sets in a concise manner.

## Lesson Summary

Let’s review. Sets are seen in everyday life. While we may not actively think about set notation when we go through our everyday life, sets and their union are there.

A **set** is simply a collection of items or numbers with each item listed only once. The **union** of two or more sets is the combination of all the items with each item listed only once.