Lesson video

Hello, and welcome on this lesson on set notation part one with me miss.

Oreyomi.

For today's lesson, you will needing your paper and your pen or something that you can write on and with.

Should you need to pause the video at any time during the lesson then feel free to do so, if you need to rewind as well to further understand something, please do so.

When I tell you to pause the video and attempt a task also, this gives you an opportunity to fully grasp what I'm saying.

So again, pause the video when I do tell you to pause the video.

Now, if you need to pause the video to go get your equipment or put yourself in a space with less distraction, pause the video now and press play when you're ready to continue with the lesson.

Okay, for your Try this task, you are to use three different numbers in the space where there's factors of, factors of and factors of, put in three different numbers.

Is it possible to have more numbers in this grey section than in any other section? So meaning every section must have at least one number.

Is it possible that the grey section has more number than every other section than any other section? So pause the video now, attempt this and come up with an answer.

Whether or not it is possible to have three different numbers so that the grey section has more numbers than any other section.

Pause the video now and attempt this and press play when you're ready to go over the answer.

Okay.

I am going to, the three numbers I'm going to work with are 10, 12, and 15.

If I start by writing the factor of 10, if I start by writing the factors of 10.

So that will be a one and 10.

That will be two and five, 12 would be one and 12, two and six, three and four and 15 will be one and 15 and three and five.

So if I am filling in the grey section, the number one is the same all the way through one, one, one.

So that goes in my grey section there.

What of the rest.

I know that five is the same for both 10 and 15.

So 10 and 15 is this section here.

So I am going to write the number five.

Hopefully you can see that.

four, 15 and 12, the number three is the same.

So over here, I am going to write the number three.

For 10 and 12, the number two is the same.

So over here, I am going to write the number two and I believe that is all.

So I am going to fill in the rest.

So I've got one and 10 and two and five for my factors of 10, that's correct.

For my factors of 12, I've got one, two, three.

So I've got 12 here and also six here.

And then from my factors of 15, I've got one, three, five.

So I've got 15 here.

So, I could only put the number one in my grey section.

So my grey section has only one number.

It is not possible for me to have three different factors or three different numbers, in this case, my numbers being a factor of something, and then have the grey section being more than any other section.

Let us think about then the different sections in a Venn diagram.

What are they called? So if I labelled this circle A and I label this circle B, if I say set notation, remembering that this is the full data have been given.

That's my wiggly E that means universal data.

So this is all my data.

Assuming I now have A, this is called intersection.

So when you see a sign like this for Venn diagram, it's called the intersection.

So I want the intersection of A and B.

So that is going to be this middle bit where they overlap here.

So this here is my intersection of A and B.

So if you want to pause the video and make notes, as I'm going along, please feel free to do so.

Now, if I change the colour and I want this U ish symbol, and this means the union, the union of A, that means A or B, this can be written as A and B, and this can be written as A or B.

So if it's A or B, that means, well, any data here.

So even going through the overlap as well, this is A or B.

So any information in both circles count as A or B.

Any information in the intersection of A and B counts as just A and B.

Now, if I've got A and an apostrophe next to my A, that means the compliment of A.

That means any data that is not in A, so I am going to try and rub some of the blue out.

So any data that is not in A would be my compliment of A, so it would be all of my B bar the overlap, cause the overlap still counts as data for A, data set for A, so I am just going to mark shade, this B in, but I'm also going to shade outside because the data inside my rectangle does not count for A or B.

So it's a compliment of A.

So I am going to shade parts of B that doesn't overlap with A, and also the outside of my circles as the data in my rectangle is a compliment of A, so it's not A, okay? So this can be thought about as not A.

Let's do the same for B then, if I want to find, if I want to shade in B compliment, well it's going to be the opposite, isn't it? It's going to be the opposite of what I've just done right now, I shouldn't have rubbed that out, cause that still counts.

So if I want B compliment, well, this is A, isn't it? And this is B.

So I am going to shade in all of A, apart from that overlap I am not going to shade in this B here, cause that still counts as a data set for B.

And I'm going to, again, just shade where my rectangle is because that counts as data that is not B.

So this is me just rush shading my Venn diagram.

You can make yours a lot neater.

So this green bit here where I've shaded, it is known as the dataset that is not B.

How about you have a turn now.

Let's put it into practise with numbers inside of Venn diagram.

How many numbers are in the sets? How would I pronounce this? A intersection B.

How many numbers are in my intersection of A and B? Well it's one, two, three, four, isn't it? So A and B, assuming this is A and this is B would be four.

How many data are in A union B? So remembering that this is union.

So A or B.

I'm going to count all of the numbers in my Venn diagram, in this circle including the numbers in the overlap section.

So this is one, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

So I have 12 numbers that are in A union B.

What of the numbers that are in A dash or A compliment.

Remembering that compliment means it is, remembering that compliment means it is not in A, so not in A, well I'm not going to count any of the numbers in this circle.

So I'm going to count one, two, three, four, five, six, seven, eight, nine, 10.

So all the numbers that are not in my A dataset are 10.

What of B, numbers that are not in B.

Let's count again.

Again, I'm not going to count the numbers in this overlap because they still count as the B dataset.

So I'm going to count one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14.

So, numbers not in B is 14.

Okay, so now we have a three way Venn diagram.

If I just label each set, this is going to be set A, this is going to be set B and this is going to be set C.

And I want to work out how many numbers I have in A union B union C, remembering that union means or right? So I want the numbers in set A or in set B or in set C.

So if I count it together I've got one, two, three, four, five, six, seven, eight, nine.

So there are nine numbers in sets A, B and C.

Right next one then, I want the number in the intersection of A, B and C, remembering that that symbol here means the intersection.

So it means where are they all meeting? They're all meeting at this point here.

So the numbers in my intersection are one and nine.

So I've got two.

Two numbers in the intersection of A, so this is circle A over there, this is circle B over there, and this is circle C here, and they all meet at that shaded region.

Next, I want the intersection of C and B.

So if I just pick the colour blue intersection of C and B, well, that is this region over here, because this is where B meets with the circle of C.

So I have again, one number in the intersection of C and B.

Next, I want the numbers in A or B, A or B.

That means all the values, all the numbers in my A and all the values in my B.

I am not going to include 11 and 12, because that is specifically for C.

So if I count the numbers in A or B, I've got one, two, three, four, five, six, seven.

So I've got seven over there.

Now, I want the numbers that are not in B, not in B.

So, lets remove some of these.

So not in B means not here.

So I'm going to have one, two, three and four.

Because the rest are in B.

So I've got one, two, three, four.

So, remembering that that dash means compliment, B compliment is how we pronounce this.

So we want the numbers that are not in B, and they are four.

Your turn, pause the video and answer the question on your screen.

How many numbers are in the sets, and then you have four options there.

So pause the video now and attempt the four questions, and then press resume when you're done with that.

Your turn, so I am going to label this as A, and I'm going to label this as B.

How many numbers are in the sets, and then you have four questions over there.

So pause the video now and attempt this, and then press resume when you are done with answering the question.

Okay.

So I am looking for the numbers in A union B.

A union B is this intersection here of A and B, and then their two numbers.

If I ask you to list the elements, list the numbers in A intersection B, you are going to draw your wiggly line and write three, seven.

Okay, how many numbers are in, let's go back to red.

How many numbers are in A union B, it's going to be all of this, isn't it? All of this right here, including the overlap.

So it's going to be one, two, three, four, five, six.

So I am going to have six here.

Again, if I tell you to list the elements, the data, and the data set A union B, what are you going to write? You're going to write 11, 15, 13, three, seven and 17.

It doesn't matter the order.

The numbers are just there.

Now, if we go for A compliment, which means not A, so dataset that are not A would be 17, nine and 19.

So that would be three numbers and not B, it'd be 11, 15, 13, 19 and nine, so those are five numbers.

Remember, if you think this has been a bit too quick, then pause the video, rewind, watch again, until you understand it better.

It is now time for your independent task.

I want you to pause the video, attempt all of the questions, and then once you're done, press resume, I will go over the answers.

So pause your video now and attempt your independent task.

Okay, I wonder how we got on with that.

I thought this task was quite good to help you to know the vocabulary to use when you're talking about certain rotation, as I think it's very important for the rest of this unit, to be able to use the correct vocabulary.

So this shaded yellow bit is the intersection.

So the keyword here is intersection of the red and the blue circle.

So it's an overlap.

The overlap is the intersection of this red circle and this blue circle.

For these two, we haven't done it yet.

You will see it later in the unit.

However, we could say the blue is the subset.

Blue is the subset of red, and therefore red is the subset of blue.

Don't worry too much about this now, we will learn this later.

Right, the shaded yellow for both circles, and I'm on this question here, the shaded yellow is the union.

So it is this symbol here.

It is the union of the red circle and the blue circle.

Okay, remembering that A intersection B is this, so this is our intersection.

And then our union is, is not U, it looks looks like a U, is this, and this is called the union.

Okay.

This next question then, the shaded bear is the compliment of A com plea ment of A, say O of the red circle.

Okay, so just a reminder again, that this apostrophe symbol here means the compliment of the dataset.

A, B, C, D are the elements.

So that means the number or the information in a list.

So the A, B, C, D are elements, Remembering that elements can, a data set can have any element.

So we've seen mostly numbers in our dataset.

However, you can have colour of eyes, height, you can have favourite food, you can have where you like going.

So your dataset can contain any sort of elements.

It doesn't have to be numbers.

And as long as your element, so if I just do an example of here, your elements are separated by commas, so I could have blue here, I could have red here, I could have yellow here.

And these are all elements of a dataset.

Right, if we move on to the next one, and we just want a couple of example, the union of A and B, well, this is all of this circle and all of that circle, but not including the C.

So I would choose, an example would be 15 or five or 10.

So I could say an example can be 15, five or 10.

The compliment of B where I could choose any number that is outside of my circle here.

So I could say number nine, I could say 15 again, cause 15 does not count as an element in B, 12 does not count as an element in B, 6 does not count as an element in B.

The intersection of A, B and C, well, there's only one number in our overlap for A, B and C in the intersection of A, B and C.

So we're just going to write the number one over there.

Okay, let's look at your explore task.

We've got cards, A, C not A, not B or rather compliment of A compliment of B, B intersection C compliment and union.

We want to use these cards to make statements.

So, if you feel like you know what to do, pause the video now and attempt your explore task, if you would like a bit more support then carry on watching the video.

Okay.

I want to use some of these cards to make a statement.

So I'm going to give you one example, and then you're going to get a chance to do this yourself.

So, if I say, A compliment and B compliment refers to the region numbered, well, they going to refer to the region number one, isn't it? So the data set that are not in A and the data set that are not in B would refer to either the region numbered one or the region numbered eight.

So pause the video now, using the cards on your screen to have a go at coming up with statements or coming up with putting the cards in this section here to complete Zaki's statement.

We have now come to the end of today's lesson.

I do hope that you remember the vocabularies today.

So the key vocabularies are intersection, dataset, element, union, and this would really put you in good stead for the rest of the lessons in this unit.

Do complete the quiz again before you leave today, as that helps you again to remember what you've done in today's lesson, and I will see you at the next lesson.

Bye.