Lesson video

Hi, I'm Missus Dennett.

And in today's lesson, we're going to be finding the union of two sets in a Venn diagram.

In this Venn diagram, one circle represents blue shades and the other represents triangles.

What does the shaded section represent? Both circles are shaded.

The section represents both shapes that are blue.

Those that are triangles, all those that are both.

This is called the union of two sets.

We represent the union of two sets using this notation.

A ⋃ B.

Here is a question for you to try.

Pause the video to complete the task and restart when you have finished.

Here is the answer.

A ⋃ B includes circle A, circle B or both.

Here is another question for you to try.

Pause the video to complete the task and restart when you have finished.

Here is the answer.

It may be useful to list all the factor pairs of 24 before starting this question.

Then look at the overlap.

We need to find the odd factors of 24.

Look at your list of factors.

One and three, go in this intersection.

We put any remaining odd numbers in the section of circle A remaining.

Then replace all of the factors of 24 that are not odd in the remaining section of circle B.

Finally check the universal set for any numbers that we haven't used yet.

10, 14, 16, 18, 20, and 22 are left.

We put these inside the rectangle, but not inside the circles 'cause they aren't odd or factors of 24.

For part B, we want to find A ⋃ B.

This is all of the numbers inside circle A, circle B or both.

It's quite a long list.

So make sure that you haven't missed any.

And remember to write them in curly brackets.

Let's recap some important Venn diagram vocabulary.

Can you remember what this shaded region represents? This is the intersection.

This would indicate that a shape is blue and a triangle for this particular Venn diagram.

We write A ∩ B.

Here's a question for you to try.

Pause the video to complete the task and restart when you have finished.

Here are the answers.

For part A, we list in curly brackets, all of the numbers in circle B.

Next we're asked to find the intersection.

This is the overlap.

Only 12 is in A ⋂ B.

Finally, we're asked for A ⋃ B.

We list all of the numbers in circle A or circle B, including 12, which is in both.

We only write 12 once though.

Take care not to duplicate 12.

Here is a question for you to try.

Pause the video to complete the task and restart when you have finished.

Here are the answers.

The first is wrong because set A includes all of the numbers in circle A.

The second statement is also incorrect.

A ⋃ B must also include the overlap as well as the numbers in circles A and B.

So three and six should also be included in the onset in the curly brackets.

Here we have a Venn diagram with three overlapping circles.

We've got set A, set B and set C.

Firstly, we're asked to find A ⋂ B.

The elements in set A and set B.

These are the elements in the overlap of the two circles, labelled A and B.

They are five, seven, and three.

Next, we want to find the elements of B ⋂ C.

We find the circles labelled B and C.

And look for the overlap, which represents the intersect.

So the elements of B ⋂ C are two and three.

Now let's look at A ⋃ B.

Find the circle A and the circle B.

All of the elements in A and all of the elements in B.

This is one nine, five, seven, three, and two.

I have listed them in numerical order.

Finally, we want to find A ⋃ B ⋃ C.

So this is all three circles.

And you can see the numbers in all three circles have been listed in numerical order in the curly brackets here.

Here is a final question for you to try.

Pause the video to complete the task and restart when you have finished.

Here are the answers.

For part A, we need to find A ⋃ B.

We list all of the letters in these two circles.

Next, we find A ⋂ B ⋂ C.

That is where all three circles overlap.

Only the letter I is in this section.

For part C, we look at A ⋃ B.

So all of circles A and B.

Then, however, we only want the parts of the circles that also intersect with C.

This leaves us with H, I and J.

That's all for this lesson.

Thank you for watching.