NomanSaleem wrote:

Question:

Total= 100 students, Physics=40, Sociology=30, Music=60. All courses=6. P+S=12, S+M=10, M+P=15. How many take none?

If we do this with formula: Total= P+S+C - (PS+PM+SM) - 2(All) + Neither, we get 19.

100=130-37-12+N

100=81+N

N=19

But if we do this with Venn Diagram we get 1. (As shown in the attached photo)

N= 100- P-S-M

N= 100- (19+14+41+6+6+4+9)

N= 1

Can anyone get the same answer with both methods?

We will get 1 in both the methods.

(P U S U M) = P + S + M - (PS + PM + SM) + PSM + Neither

100 = 40 + 30 + 60 - (12 + 15 + 10) + 6 + Neither

100 = 136 - 37 + Neither

Neither = 1

You made a mistake by doubling and subtracting the overlap (among the three) instead of just adding, hence the mismatch between formula and Venn diagram.