Lesson video

Hi, I'm Mrs Dennett.

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

In this Venn diagram, one circle represents blue shapes, one represents triangles and they overlap.

We call this the intersection of the two sets.

It's where the blue shapes that's what also triangles go.

We represent the intersection using this symbol.

So for the intersection of sets A and B we say, A intersect B.

On the diagram, this is the shaded part where the two circles overlap.

To list the elements of A intersect B.

We need to identify the correct region.

This is where the circles overlap.

We use curly brackets to show A intersect B equals one three.

Here's a question for you to try.

Pause the videos to complete the task and restart the video when you're finished.

Here are the answers.

The members of set A are all of the numbers in circle A.

Rewrite this in curly brackets in any order.

We then do the same, but for all of the numbers in circle B.

To find A intersect B look at the overlap of circles A and B.

The numbers in this section are six and 12.

Here's a question for you to try.

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

Here were the answers.

The question two, start with the overlap.

Two and six are even and factors of six.

Now, look at the remaining section of circle A.

The only remaining even number is four.

We then put the remaining factors of six in the set B, but not in the overlap as one and three are odd.

Finally, place five in the rectangle, but outside of the circles, as it is the only managing member of the universal set.

For part B, we look for A intersect B.

This is the overlap, two and six are the only elements in this section.

Remember to use curly brackets when writing this answer.

The part b, by looking for even numbers that are also in set B, these are six, 12, 18, and 24.

Here's a question for you to try.

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

Here are the answers.

Start by filling in the overlap for sets A and B.

We are told, A intersect B contains four and 16, put these numbers in the intersection of the overlap.

To fill in the remaining parts of circle A, we need to use the information given to us about the universal set.

The set contains the numbers one to 16, including one in 16.

So look at the diagram to work out which numbers haven't yet been used.

Go through the numbers in ascending order so that you don't miss any.

One is already in circle B, two isn't in the diagram.

So put it in the remaining section of circle A.

Three, four, and five are already there, but we need to put six in the remaining section of circle A.

Continue in this way, until you have included all of the numbers in the universal set.

When drawing a Venn diagram, we can also just write down the total number of items in each region.

Instead of putting in three blue circles, I could just write three.

I can do this for each region of the Venn diagram.

In this question, we have a class of 30 students, 12 own a cat, eight own a dog and three own a cat and a dog.

When it says 12 own a cat, it doesn't mean they only own a cat, they may have a dog as well.

Let's complete the diagram, always start with the overlap or intersection if you can.

This section represents those who have a cat and a dog.

There are three of these.

We know that 12 students own a cat.

So the total for the cat circle is 12.

Three have already been used up.

So we have nine left.

We know there are eight students in total who own a dog, again, three being used up.

So we calculate eight take away three leaving us with five students who only own a dog.

If we add up nine, three and five, we get 17, but we know that there are 30 students in the class.

So the other 13 students must not on a cat or a dog, we put 13 in the rectangle.

Here's a question for you to try.

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

Here are the answers, to work out how many students study French? We look at the French circle.

We can see there are seven students who only study French and five who study French and Spanish.

Seven and five is 12.

So there are 12 students who study French.

The section representing students who study both languages is the overlap or the intersection, there five students here.

Finally, we want to find the number of students who do not study a language.

We look for the region outside of the circle, both circles that is, and you can see that there are 140 students here.

That's all for this lesson.

Remember it's completely exit quiz.

Thanks for watching.