# Maths Venn Diagram Set Problem

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Thread starter 3 years ago
#1
Hello, I am struggling to solve this question. I am usually fine at solving them but this particular question I am not sure how to approach.

There are 37 science students in total, all take at least one of chemistry, biology or physics. 24 take chemistry, 35 take biology and 18 take P ∩ C ∩ B. 10 students take biology only.
Find how many students take chemistry only and how many altogether take physics.

I do not really know how to solve this, any helped would be appreciated .
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3 years ago
#2
(Original post by JS547)
Hello, I am struggling to solve this question. I am usually fine at solving them but this particular question I am not sure how to approach.

There are 37 science students in total, all take at least one of chemistry, biology or physics. 24 take chemistry, 35 take biology and 18 take P ∩ C ∩ B. 10 students take biology only.
Find how many students take chemistry only and how many altogether take physics.

I do not really know how to solve this, any helped would be appreciated .

May be wrong, but I don't think it's solveable as is. Can you provide a link or image of the original question - there may be something in the exact wording that allows you to deduce further information.
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Thread starter 3 years ago
#3
It is the third part of a question but I do not think you need the other parts to solve it.
The first question has a empty Venn diagram of the three science subjects. If the universal is all students then P= physics, C = chemistry and B=biology. Copy the Venn diagram and write 0 in the appropriate regions, the two subsets of the universal set that are empty as a result of :
a) all students taking physics and chemistry also take biology
b) no student takes physics only

The second part asks you to find the single set equivalent to P∩B.

ghostwalker
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Thread starter 3 years ago
#4

This is the exact wording of the question.
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3 years ago
#5
(Original post by JS547)
It is the third part of a question but I do not think you need the other parts to solve it.
The first question has a empty Venn diagram of the three science subjects. If the universal is all students then P= physics, C = chemistry and B=biology. Copy the Venn diagram and write 0 in the appropriate regions, the two subsets of the universal set that are empty as a result of :
a) all students taking physics and chemistry also take biology
b) no student takes physics only

The second part asks you to find the single set equivalent to P∩B.

ghostwalker
From what you've put, I think that parts a and b are relevant. It allows you to put zeros in some of the areas, allowing the deduction of the rest.
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Thread starter 3 years ago
#6
(Original post by ghostwalker)
From what you've put, I think that parts a and b are relevant. It allows you to put zeros in some of the areas, allowing the deduction of the rest.
Ok, I thought that c) was a seperate question just within the same topic of Venn diagram/set work.

For a) and b)
Would the second statement mean there should be a 0 is the physics only section?
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3 years ago
#7
(Original post by JS547)
Ok, I thought that c) was a seperate question just within the same topic of Venn diagram/set work.

For a) and b)
Would the second statement mean there should be a 0 is the physics only section?
Yes.
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Thread starter 3 years ago
#8
ghostwalker
The second statement causes the physics only subset to be empty.
The first statement ‘all students taking chemistry and physics also take biology’ is why I have shaded the subsets blue that are the combination of chemistry and biology, physics and biology.
Would the subset between Physics and Chemistry be where the second 0 needs to go because ‘ALL students taking chemistry and physics ...’ therefore there are no remaining students to take the combination of physics and chemistry?
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3 years ago
#9
(Original post by JS547)
ghostwalker

The first statement ‘all students taking chemistry and physics also take biology’ is why I have shaded the subsets blue that are the combination of chemistry and biology, physics and biology.
Would the subset between Physics and Chemistry be where the second 0 needs to go because ‘ALL students taking chemistry and physics ...’ therefore there are no remaining students to take the combination of physics and chemistry?
Yes.

All students taking C and P also take B. So, there are no students in the C and P and not B part of the diagram, i.e. 0.
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Thread starter 3 years ago
#10
ghostwalker
Would this be how it would look?
I agree with no students in C and P but I thought that there would be students in B because it do not believe either of the statements express that there will be no students who only take Biology. Additionally the question only asked which two subsets are empty as a result of the statements. Also, in part 3 it mentioned that 10 students take biology only.

There was another question asking which single set was equivalent to P∩B would it be P∩B∩C’ ?
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3 years ago
#11
(Original post by JS547)
ghostwalker
Would this be how it would look?
I agree with no students in C and P but I thought that there would be students in B because it do not believe either of the statements express that there will be no students who only take Biology. Additionally the question only asked which two subsets are empty as a result of the statements. Also, in part 3 it mentioned that 10 students take biology only.
I'm not really clear what you're asking.

From what you've said of the other two parts of the question, there are two areas of the Venn diagram with zero students - in addition to the large external area.

In part c), yes, there are 10 students taking Biology only.

The bit you've coloured blue - i don't know what that's meant to represent, even from your previous description. Not sure what relevance it has. Confuses rather than clarifies.

It is also possible that the combination of values given in part c, may mean there are other areas with 0 students when you come to work out the values.
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Thread starter 3 years ago
#12
(Original post by ghostwalker)
I'm not really clear what you're asking.

From what you've said of the other two parts of the question, there are two areas of the Venn diagram with zero students - in addition to the large external area.

In part c), yes, there are 10 students taking Biology only.

The bit you've coloured blue - i don't know what that's meant to represent, even from your previous description. Not sure what relevance it has. Confuses rather than clarifies.

It is also possible that the combination of values given in part c, may mean there are other areas with 0 students when you come to work out the values.
Sorry I do not mean to be confusing. I was trying to ask if the subsection if biology only was empty.

I coloured the subsections blue because of the second statement which was saying ‘all students taking physics and chemistry also take biology’, so I was trying to rule out any of those areas being empty more so through a visual aide.

Yes, I agree with there possibly being more empty subsections, I was only looking for the two loosely outlined in the statements just because it was answering that part of the question.

Additionally, I was not sure if the biology only was empty because you had to find the information from the statements, which I did not think gave any clear evidence as to biology only subsection being empty, though I may be wrong.

ghostwalker
0
3 years ago
#13
(Original post by JS547)
Additionally, I was not sure if the biology only was empty because you had to find the information from the statements, which I did not think gave any clear evidence as to biology only subsection being empty, though I may be wrong.

ghostwalker
Biology only isn't empty - question says there are 10 in there, so you can fill that in straight away.
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Thread starter 3 years ago
#14
(Original post by ghostwalker)
Biology only isn't empty - question says there are 10 in there, so you can fill that in straight away.
Thank you.
Even though I now know that there are 10 students in biology only, 0 in P∩C and Physics only and 18 in the center I do not know if I have enough information to find the other values?
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Thread starter 3 years ago
#15

Is this how part 3 would look.

Then is B = 35
10+18 =28
35-28= 7 split between P∩B and C∩B

C=24
24-18 =6
6 split between Chemistry only and C∩B

37-28=9
9 students left in the universal
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Thread starter 3 years ago
#16

I think this is the answer, because there were 6 unaccounted students in chemistry and 7 in biology and 9 overall.
There are 0 students to in Chemistry because of the first statement, so the only place left for the remaing chemistry students was subsection C∩B.

To answer the question, zero students take chemistry only and 19 students take physics altogether.
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3 years ago
#17
(Original post by JS547)

Is this how part 3 would look.

Then is B = 35
10+18 =28
35-28= 7 split between P∩B and C∩B
If I use ' to represent the complement of a set then that should be:

7 split between PnBnC' and CnBnP'

C=24
24-18 =6
6 split between Chemistry only and C∩B
Should be Chemistry only and CnBnP'

37-28=9
9 students left in the universal
Don't know what you mean by that. If you mean outside all three circles, then no, since that is empty - everyone takes at least one subject.

You may find it helpful to focus on BuC, which contains all 37 students. So, BnC is....

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