Mathematical Sets- Elements, Intersections & Unions

A set is a collection of objects, and it doesn’t need to be a number!

This is the set of the clothes in my closet: C = {pants, t-shirt, skirt, and dress}.

The capital C represents the set.

So, if I said set C , we know I’m talking about clothes in my closet.

The braces, { }, denote the elements, or members of the set.

The elements of set C are pants, t-shirt, skirt, and dress.

You’re probably familiar with a set of real numbers.

The three dots indicate that the pattern continues.

The elements of this group are all real numbers.

So, R equals the set of real numbers.

To collect sets together, we use the term union .

We unite the sets into one.

Let’s say I have two sets.

Set A is green, blue, and pink.

Set B is orange, yellow, and black.

A u B represents the union of sets A and B .

and yes, that u symbol represents union!

It’s kind of handy!

A u B represents all the elements that are listed in set A , or in set B , or in both.

How would that look in using mathematical symbols?

A u B = {green, blue, pink, orange, yellow, black}.

To find elements in common with sets, we use the term intersection .

Think of the sets as two roads that meet at an intersection.

What do the two roads, or sets, have in common?

Let’s say I have two sets.

Set A is 4, 6, and 9.

Set B is 7, 8, and 9.

A intersect B represents the intersection of sets A and B .

Yes, that upside down u represents intersection!

This represents all the elements that are the same in A and B .

How would that look in using mathematical symbols?

A intersect B = {9}.

Let’s review what we just talked about.

A set is a bunch of objects.

It could be numbers, letters, anything.

To show a set, we always use a capital letter.

To show the members, or the elements, of a set, they always go between braces, { }, or these curlicue parentheses.

Union is when we unite things - when we’re going to put things together.

So, A u B means that we’re going to put everything in A together with everything in B .

Remember, intersection is where things are the same, where they intersect at.

So, if I say A intersect B , what I’m looking for is any elements, or members, that are common in A and B.