Lesson video

Hi, I'm Mrs. Dennett and in today's lesson, we're going to be finding the complement of a set.

Here's a Venn diagram.

We can see that the universal set contains the numbers one to 10.

Set A contains only even numbers, and set B contains elements one, two and nine.

We're going to find the complement of set A.

This means that we want to find all the elements of the universal set that are not in set A.

I've covered up the numbers in set A.

This shaded blue region is the complement of A.

We write A with a dash equals five, seven, one, nine and three in curly brackets.

These are all of the elements not in set A.

Similarly, we can find the complements of set B, cover up circle B, and write down all of the elements not in circle B.

These are five, seven, six, eight, four, 10 and three.

Remember to write your answer in curly brackets.

And then we have the complement of set B.

Here's a question for you to try.

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

Here are the answers.

You can see that we haven't shaded in circle A for each of these questions.

Even when another set is inside set A or overlaps with it, we don't shade it as elements of A will be within that region.

Before we continue, let's recap some more important set notation.

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

We write A intersect B like this.

What about the bottom diagram? What does the shaded section represent? Circle A and circle B are shaded.

We call this the union of two sets, sets A and B, and we write it like this.

Here's a question for you to try.

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

Here are the answers.

To find the complement of B, cover up all of circle B and list the remaining numbers of the universal set.

A union B is all of the numbers in circle A or B, or the overlap.

To find A union complement of B, we look at all the elements of set A or the elements of the complement of B.

12 is in set A, so it's included in our answer.

The only section we don't include is the remaining section of B.

So we don't include three, six or nine.

To find A intersect B, we look at elements of A and B.

Only 12 is in this part of the Venn diagram.

Finally, we want the complement of A intersect B.

This is the opposite of Part D.

Include all of the numbers in the universal set except 12, which is in A and B.

Here is a question for you to try.

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

Here are the answers, start with the overlap of Q and R.

Two, four and six are in both sets.

So put them here.

In the remaining section of Q, put eight, and then one and three are the remaining elements of R.

Check the universal set for any remaining numbers that aren't in sets Q and R.

Put these inside the rectangle but not inside the circles.

Then look for the complement of Q.

Any numbers not in circle Q needs to be included in this list.

They are one, three, five, seven and nine.

Here is a question for you to try.

We can't really draw a Venn diagram for this question because we're not given the universal set.

However, you may find it useful to sketch one to help you.

Think about the position of certain numbers and where they may go in the Venn diagram.

I will also read out Parts a and b, in case you're not familiar with the notation being used.

True or false, Part a, nine is an element of S intersect T? Part b, 16 is an element of the complement of T? Pause the video to complete the task and restart when you are finished.

Here are the answers.

For part a, we want to know if nine is a member or number in the intersect of S and T.

Any number in S intersect T would need to be a square number and a multiple of three.

Nine is a square number and a multiple of three.

So it will be in S intersect T.

For part b, think about the complement of T.

This will be any number that is not a multiple of three.

16 is not a multiple of three, so it is not in set T and must therefore be in the complement of T.

Here is a final question for you to try.

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

Here are the answers.

When completing a Venn diagram, always start with the overlap where possible.

This is the students who study economics and statistics.

Five students go here.

We don't know how many students study only economics so leave this section for now.

Instead, we can fill in the remaining section for students who only study statistics.

15 students only study statistics.

Finally, 44 students don't study economics or statistics.

So these students go in the rectangle.

We know that there are 90 students in total and if we add up five, 15 and 44 we get 64.

This means there are 26 students remaining who must study only economics.

Now we have filled in the diagram, we can work out how many students do not study economics.

This is like finding the complement of set E, the economic circle.

We cover up the circle E and add together 15 and 44 to get 59 students who do not study economics.

That's all for this lesson.

Remember to take the exit quiz.

Thank you for watching.