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Hello, and welcome to this lesson on overlapping circles with me Miss Oreyomi.

For today's lesson you will be needing a paper and a pen, a pencil might come in handy when you're drawing your Venn diagrams, however, it is not necessary for today's lesson.

Also, it would help if you are able to be in a space with less noise and distractions just so that you could focus on today's lesson.

If at any point during today's video, you want to pause the video just to further, to just take some longer time to understand what I've just said, or if you want to rewind the video, please do so by all means.

Also, if at any point I told you to pause the video to do a short task, again do so cause that would help you to further understand what I've said.

So, if you need to pause the video now to go get your equipment or to put yourself in a space with less noise, then please do so and press resume when you're ready to begin the lesson.

Let's think about our try this task.

I've got four circles here representing four data set.

Can you describe a name the regions that are not shown in this Venn diagram.

So which region can you not see? And then once you've had a go at that, once you've thought about which regions you can't see, can you draw a Venn diagram with four sets that shows every region? So pause the video now, think about this question, try to attempt to draw a Venn diagram of four sets and then press play when you're ready to resume the lesson.

Okay, when I was thinking about this task, I noticed that I couldn't see the region B intersecting D on its own.

If so this is B, I could see a part of A I could see a part of C, however, I couldn't just find a region that was dedicated just to the intersection of B D, nor could I see a region, I wonder how you got on, did you notice anymore? I couldn't see a region that was dedicated again to the intersection of A C.

So if I wanted to find him data on C, I would have to get some data on D some data on B, before I got some data on C.

So, did you manage to come up with a Venn diagram of four sets that shows every region? This is an example of one.

So instead of circles like so, we now have oval shapes, cause circles are quite limiting in the sense that they don't show every region as we just seen, however, we have an oval.

So assuming this is a data set B, set B, this would be the set D, I could see ah, this is the intersection of B and D.

So I don't need to get data on A or C or anything like that.

Again, assuming this is set A and this is C, I could just get this information right there for the intersection of A and C.

How does that link into today's lesson then? Well, let's read the sentence on our screen.

Given A is, so set A has the elements one, two, and four, and B has the elements one two three four and five, what is the relationship between the sets? If I want to draw this Venn diagram representing this information, I would do something like this, I would have one two four and this would be my set A.

Have you noticed what is in set A and what is in set B? Are there any other any elements that are the same? Right, I've got elements one two and four in A and I've got the same element one two and four in B.

So, instead of drawing another circle there, I could do this and just add three and five for set B.

So essentially I am saying set B has got the non elements one two three four five, and A is therefore, a subset of B.

So, something like this it means A is a subset of B.

That means, every element in set A is in set B, that's what I mean by subset.

It means every element in A is also in B.

Notice how, I'm just going to change the colour, notice how this is different from this.

So for example, if I have A is one two, and B has got four three and five, notice how the only element that is the same for A and B in this one is just four, so A is not a subset of B in this case.

A is only a subset of B or rather a set as a subset of another when every single element in that set is also in the other set.

Let's take another example.

I've got this one, A is got the numbers one three five four and two, and B is got the element one two three four and five.

What do you notice? Hopefully, you've seen that regardless of whether it's ordered or not, these elements are exactly the same as these element.

So, I could draw a circle like so for elements A, and I'm just going to get a different colour pen, it should be a perfect circle and I'm just going to go round my first circle like so, saying A and B has got the elements one two three four five.

So in this case, A is a subset of B, and B is a subset of A.

Therefore, A and B are equivalent.

They're the same, they have the same data set in the set, they have the same elements in this set.

So here means A is a subset of B, and here B is a subset of A meaning, each data, each set has the same element.

And therefore, A is equivalent to B.

Right, you are to list all the subsets of the set C, that means what sets can you have that would be a subset of C or that can be a subset of C? Well, if I start with D, and I say the element in my set D is just the number one.

Well, if I try to draw that as a Venn diagram to show the relationship between set C and set D, this would be my set D, just having the element one, and then set C would have two and three in it.

So yes, D equals to one, one being an element inside of D is a subset.

What if I say, E and I say an element in my set, the only element in my set E is two.

Well again, if I write the number two here, I changes these to a one.

Yes, he is a subset of C, what will be another one then? Well, I could say three is here, and the same thing would happen, F is three, so therefore my set C, we just have the numbers one and two in it.

What if I say my G has elements of one and two, my H has got elements of two and three, my I has got elements of one, two and three.

So this here shows us that every set is a subset of itself.

So I've got the numbers one two three, this is a subset of GI one two three, cause it's got the exact values in it.

What if I say, so I've got one two three four five six, and if I have, am I missing any other, yes, so if I say K is three one or one three, again, if I should draw the relationship between K and C, K here would be one three, and C would only have the number two in it, so I can say K is a subset of C.

There's another one we call null.

There's nothing in null, that means the null sets can't have anything that isn't contained in C.

So if there's nothing here, I can't have anything that isn't contained in C, so therefor the null is a subset of C.

So I've got one two three four five six seven eight, and these are my subsets, these are subsets of set C, these are all the subsets for set C.

How about you pause the screen now and have a go at this one.

I want you to list all the subsets of set C, when C has got elements one two three four.

So list all the subsets of set C, when C has got the elements one two three four, and then choose one of your subset and show the relationship between that subset and C.

So pause the video now and attempt this task and press resume to go over the answer.

Okay, I hope you thought about that, and I hope you came up with something that looks like what you have on your screen, so I have this table here, and then list all the subsets of C.

So if I want to draw a Venn diagram that shows the relationship between set C and set P, I would have something like this.

This would be my set P, and we would have the numbers one two and four, my set C would have the number three in it, And I could say, yes, P is a subset of C.

It is now time for your independent task.

I want you to pause the video now and attempt every question on your sheet, and then once you're done, press resume to go over the answers.

So pause the video now and attempt all the questions for your independent task.

Okay, welcome back.

How did you get on with those questions? I have gone ahead and put the answers on the screen, so I'm just going to be talking through them with you.

So question one, list all the subsets of the set T and the elements in set T are x, y and z, how many subsets are there? So if you look over here at this table, I've got one two three four five six seven eight remembering that this is our null, N-U-L-L.

I'm just going to write make that neater, so this is an N-U-L-L, so how many are there? There are eight subsets.

Next one, let A be multiples of four, don't forget your squiggly line your squiggly bracket and B be multiples of two.

So I put my dot dot dot there to say it basically goes on forever is a subset of B.

Well the answer is no, because there I don't have exact elements that is the same as B, nor do I have exact elements in B that are the same for A.

So the answer for both is no, B is not a subset of A nor is A subset of B.

Next one, draw a Venn diagram for the following.

P is the set of factors five, so that's one and five, Q is the set of factors 25, and R is the set of 125.

So if we try and draw a Venn diagram for that, that would be P, that would be Q.

So if I start with P one five, Q would be, here 25 and R would be one five so this is P, this is Q, so R would be one five 25 and then one two five.

So R is taking on P which is one five, elements of P which is one and five, elements of Q which is 125, and then R itself which is 125.

Which sets are subsets of each other then? Well, P is a subset, I put the symbol here instead of writing subset so that you recognise the symbol for subset, so P is a subset of Q, and Q is a subset of R.

So check in, I know you've got that.

Last couple of questions, A is a set of prime numbers less than 10, again, I've gone and written that for you, B is a set of odd numbers less than 10, and C is even number less than 10.

How many subsets are there in this Venn diagram? There's none is there? No, so it's zero.

So, number five then A is the set of factor of three, B is a set of multiples of three, and C is a set of factors of three.

How many subsets are there in this Venn diagram and draw a Venn diagram showing the relationship between sets A and C.

So how many subsets are there in these Venn diagram? It's just one, isn't it? And that is A is a subset looks like a C of C.

So A is a subset of C, and I've drawn the Venn diagram here, this is A, set A, which is one and three and set C which is nine.

It is now time for explore task.

Your job is to match the categories at the bottom of your screen with the Venn diagram, find an example that fit in each part of the diagram, and can you think of other groups that fit in these Venn diagram.

So the first one is integers and prime numbers, which Venn diagram of the four you have, which Venn diagram will fit into this integers and prime numbers where the red circle would be for set integers, and the blue circle would be for set prime numbers.

Again, even numbers and multiples of two, which one of these four would fit this category? Multiples of two multiples of three, even numbers and odd numbers.

When you're done that, can you find more examples that would fit into these Venn diagrams? So pause the video now, and attempt to explore tasks, and once you're done, press resume to carry on with the video.

You've now reached the end of today's lesson, a very big well done for sticking all the way through and I hope you've learned about subsets and you know where they are.

Do complete the quiz before you leave as that would show you what you've learned in today's lesson.

But until then, goodbye.