venn diagram help pleaseWatch

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Thread starter 1 month ago
#1
i’m really confused by this whole thing...
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Thread starter 1 month ago
#2

i don’t understand... the apostrophe’s

these questions???

Sir Cumference Muttley79
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1 month ago
#3
For the first question, shade the area outside the circles.
For the second question, shade all areas except the A circle without the part in the centre.
For the third question, you only need to shade the A circle without the part in the centre overlapping A and B.
For the question 10, the probability is 44/50
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1 month ago
#4
(Original post by IH8Studying)

i don’t understand... the apostrophe’s
The apostrophe means 'complement' and in simple terms, A' is the entire region EXCEPT A. So imagine shading in the entire rectangle box but shading around the circle labelled A as to exclude it.

I also recommend you use different coloured pencils (or use different shading pattern with your pen) because then it's much clearer what your region must be.
For instance, in you would shade in A with one colour. Then shade in B' with another colour. Then since we have an 'intersection' then you just need to look where these two colours overlap eachother. Shade in this region with your pen (or otherwise clearly) as your final answer.

Use this to correct your answer to Q6.
Last edited by RDKGames; 1 month ago
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Thread starter 1 month ago
#5
(Original post by RDKGames)
The apostrophe means 'complement' and in simple terms, A' is the entire region EXCEPT A. So imagine shading in the entire rectangle box but shading around the circle labelled A as to exclude it.

I also recommend you use different coloured pencils (or use different shading pattern with your pen) because then it's much clearer what your region must be.
For instance, in you would shade in A with one colour. Then shade in B' with another colour. Then since we have an 'intersection' then you just need to look where these two colours overlap eachother. Shade in this region with your pen (or otherwise clearly) as your final answer.
oh so i don’t shade in the middle aswell? got it.

yeah i don’t think we’re allowed different colours in the exam. sorry but can you give me an example of a pattern i can use to be clearer? would highly appreciate it
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1 month ago
#6
(Original post by IH8Studying)
oh so i don’t shade in the middle aswell? got it.

yeah i don’t think we’re allowed different colours in the exam. sorry but can you give me an example of a pattern i can use to be clearer? would highly appreciate it
The middle is part of A. So since you ignore A then you automatically ignore the middle when shading in A'.

One common shading pattern would be (and i will use the same example as above) to use //// parallel line pattern to shade in A, then \\\\ parallel line pattern to shade in B'.
Then it's clear where they overlap and intersect.

Anyhow, I know you probably cant use coloured pencils in exams but Im saying you should use them while you're learning this content and once you get a hang of it then you wont need colours anymore.
Last edited by RDKGames; 1 month ago
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Thread starter 1 month ago
#7
(Original post by RDKGames)
The middle is part of A. So since you ignore A then you automatically ignore the middle when shading in A'.

One common shading pattern would be (and i will use the same example as above) to use //// parallel line pattern to shade in A, then \\\\ parallel line pattern to shade in B'.
Then it's clear where they overlap and intersect.

Anyhow, I know you probably cant use coloured pencils in exams but Im saying you should use them while you're learning this content and once you get a hang of it then you wont need colours anymore.
is this okay?

i mean its clear isn’t it?
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1 month ago
#8
(Original post by 8013)
For the first question, shade the area outside the circles.
For the second question, shade all areas except the A circle without the part in the centre.
For the third question, you only need to shade the A circle without the part in the centre overlapping A and B.
For the question 10, the probability is 44/50
No point giving away answers, especially wrong ones (your sol to second venn diagram shading is wrong) so just give hints instead and they will obtain the answer themselves.
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Thread starter 1 month ago
#9
(Original post by RDKGames)
No point giving away answers, especially wrong ones (your sol to second venn diagram shading is wrong) so just give hints instead and they will obtain the answer themselves.
i did the pattern thing like you said
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1 month ago
#10
(Original post by IH8Studying)
is this okay?

i mean its clear isn’t it?
Not super clear.

Look, shade in the A circle entirely with //// strokes.
Then shade in the entire B' region with \\\\ strokes.

Where do they intersect ?? Fill in this region by a full shading.
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Thread starter 1 month ago
#11
(Original post by RDKGames)
Not super clear.

Look, shade in the A circle entirely with //// strokes.
Then shade in the entire B' region with \\\\ strokes.

Where do they intersect ?? Fill in this region by a full shading.
0
1 month ago
#12
(Original post by IH8Studying)
oh so i don’t shade in the middle aswell? got it.

yeah i don’t think we’re allowed different colours in the exam. sorry but can you give me an example of a pattern i can use to be clearer? would highly appreciate it
Think about B' meaning not in B so A U B' means shade the area in A or not in B.

Most students find it easier to think in words like this.

U means 'or'

upside down U means 'and'
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1 month ago
#13
(Original post by IH8Studying)
I don't recommend double shading like this - use the space around the question to work out the area you are asked for and then just shade your answer on the diagram you are given.
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1 month ago
#14
(Original post by RDKGames)
Not super clear.

Look, shade in the A circle entirely with //// strokes.
Then shade in the entire B' region with \\\\ strokes.

Where do they intersect ?? Fill in this region by a full shading.
This is not a recommended approach now because of scanning exam papers before they are marked.
1
1 month ago
#15
How I understood venn diagrams is by this: (we go over this is A level Maths too and at first not everyone understood it)

First understand the basic that U means OR. ∩ means AND
When we say A U B, think this as A OR B. In Maths, this means it has to be either in A or either in B.

So in this example: A( () )B shade the regions that are A U B

Look at the first left circle(A). Think is this is in A or is it in B? We know this is in A! so we shade it.
Now look at the centre circle. Think is this is in A or is this in B? We know this is in both of them! So we shade it.
Now look at the right circle(B). Think is this in A or is this in B? We know it is in B! so we shade it in.
Now look on the outside of the circle. Is this in A or is this in B? It is in neither! so we leave it blank.

When we say A ∩ B, think is this in A AND B. In Maths, this means it has be in BOTH A and B.

So in this example: A( () )B shade the regions that are A ∩ B.

Look at the first circle(A). Think is this is A and in B? Well it is in A but it is not in B! So we leave it blank.
Look at the centre circle. Think is this in A and in B? Yes it is! So we shade it in.
Look at the right circle(B). Think is this in A and B? Well it is in B but not in A! So we leave it blank.
Look outside the circle. Is this in A or in B? Well it's not in either. So we leave it blank.

With more practice you could do this very quickly. In summary, remember that A or B means it just has to be in one of them.
For A and B, it has be in both of them.
Last edited by MathYani; 1 month ago
1
1 month ago
#16
(Original post by IH8Studying)
...
No it's not quite there still.

You are finding . So shade in first using //// strokes. You get:

Spoiler:
Show

Then shade in the using \\\\ strokes. You get:
Spoiler:
Show

And since means EITHER //// OR \\\\ then you can just fully shade in every region that has a stroked line going through. I've used a yellow highlighter on the compuiter but obviously you can just fill it in with your pen instead. You get:

Spoiler:
Show

And if the question had wanted instead, then you just shade in where the two lines //// and \\\\ intersect. You get:

Spoiler:
Show

As you can see, when you do it properly it's easy to read and not full of scribles. And just to make it very clear to the examiner or whoever it is assessing you on this topic whenever, you can put a key down such as:

(//// shading) = A'

(\\\\ shading) = B

(full shading) = A' U B
Last edited by RDKGames; 1 month ago
1
Thread starter 1 month ago
#17
(Original post by RDKGames)
No it's not quite there still.

You are finding . So shade in first using //// strokes. You get:

Spoiler:
Show

Then shade in the using \\\\ strokes. You get:
Spoiler:
Show

And since means EITHER //// OR \\\\ then you can just fully shade in every region that has a stroked line going through. I've used a yellow highlighter on the compuiter but obviously you can just fill it in with your pen instead. You get:

Spoiler:
Show

And if the question had wanted instead, then you just shade in where the two lines //// and \\\\ intersect. You get:

Spoiler:
Show

As you can see, when you do it properly it's easy to read and not full of scribles. And just to make it very clear to the examiner or whoever it is assessing you on this topic whenever, you can put a key down such as:

(//// shading) = A'

(\\\\ shading) = B

(full shading) = A' U B
so if it is U then you also shade the region outside the circles?
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Thread starter 1 month ago
#18
(Original post by Muttley79)
Think about B' meaning not in B so A U B' means shade the area in A or not in B.

Most students find it easier to think in words like this.

U means 'or'

upside down U means 'and'
i know so i shaded B when it said A’ U B. And what???? and shade everything else?
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1 month ago
#19
1
1 month ago
#20
(Original post by IH8Studying)
so if it is U then you also shade the region outside the circles?
It's not correct to say that "for any generic problem like this you must shade in the region outside the circles if we have U".

The reason we have to shade in the outside of the circles is because contains these outside regions, therefore they must be involved when considering . Hence why I simply told you to fully shade in the regions where we have at least one stroke going through, and obviously this includes the outside of the circles.

If we had , then of course we don't shade in the outside just because we have U in here. You can follow the method I have provided to deduce what this region is (if you dont already know)
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