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I have a question on three set problems using the Venn diagram.


In a class of $10$ Students, $4$ offer Mathematics, and $1$ offers Chemistry and Mathematics. $1$ offers Physics and chemistry, and $3$ offer Physics and Mathematics. Each student offers at least one of the three subjects.

If the number of students who offer Mathematics is equal to that of those who offer Physics only and $n(M)+n(C)=n(P)$, Find the number of students who offer

a) chemistry only,

b) only one subject,

c) only two subjects,

d) Physics,

e) Chemistry,

f) chemistry and physics only.



I illustrated it on the Venn diagram, but I couldn't do further. Thanks! (https://i.stack.imgur.com/YZYHC.jpg)

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    Include your venn diagram and all your work in the question. – 2017-01-12
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    This is very definitely a hw question. But it seems like it might be useful as an example for some. Anyway, try drawing dots on the Venn diagram (to represent people). Think about the different ways in which 10 people could fit in the diagram, knowing the hints you have been given – 2017-01-12
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    Thanks, I just did it finally – 2017-01-12

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![it needs a bit concentration, but here's the answer ] (https://i.stack.imgur.com/42Rrb.jpg)