Question 1149313
<pre>

Using the same interpretation as tutor @greenestamps, and borrowing the nice Venn diagram code from tutor @Edwin_M, and adding my own lettering:

{{{drawing(400,400,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"a"),
locate(0,-2.9,P),
locate(-.45,-1,"g"),
locate(.6,.4,"f"), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.7,2.5,C),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,M),
locate(-1.3,.5,"e"),
locate(-.2,2.3,"b"),
locate(1.8,2,"c"),
locate(-.2,1.1,"d") )}}}


a = Chem only
b = Chem & Math only
c = Math only
d = all 3 subjects
e = Chem & Phys only
f = Math & Phys only
g = Phys only


There are 7 equations in 7 unknowns:

1. a+c+g = 15
2. e+d = 18
3. f+d = 17
4. a+b+d+e = 25
5. c+b+d+f = 22
6. d+e+f+g = 25
7. a+b+c+d+e+f+g = 36

{{{ (matrix(7,7, 
    1,0,1,0,0,0,1,  
    0,0,0,1,1,0,0,
    0,0,0,1,0,1,0,
    1,1,0,1,1,0,0,
    0,1,1,1,0,1,0,
    0,0,0,1,1,1,1,
    1,1,1,1,1,1,1)) *
(matrix(7,1, a,b,c,d,e,f,g)) = 
(matrix(7,1,15,18,17,25,22,25,36)) }}}

Which has the solution (courtesy of http://www.bluebit.gr/matrix-calculator/solve.aspx):

a = 6
b = 1     <<< Taking Math & Chem only
c = 4
d = 15    <<< Taking all 3 subjects
e = 3
f = 2
g = 5  


This agrees with tutor @greenestamps answer.  Tutor @Edwin_McCrary has a at least one setup problem that I noticed: (referring to his diagrams)  e + g + i = 15 should be d + f + j = 15.

Best wishes.