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,
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)