Question on Set Theory
The problem statement is: "It was found that out of 100 consumers, foll. are the details of preference for 3 brands A,B and C.
(a) Brand A - 50 consumers
(b) Brand B - 40 consumers
(c) Brand C - 30 consumers
(d) Both brands A and B - 20 consumers
(e) Both brands B and C - 15 consumers
(f) Both brands A and C - 10 consumers
Find how many used all the 3 brands A, B and C?"
I used the formula (x = intersection):
n(AUBUC) = n(A) + n(B) + n(C) - n(AxB) - n(AxC) - n(BxC) + n(AxBxC)
=> 100 = 50+40+30-20-15-10+n(AxBxC)
=> n(AxBxC) = 25
Somehow, I am not convinced that the answer is correct, one of the reasons being n(AxBxC) is > n(AxB), n(AxC), n(BxC).
Can you pl. clarify/confirm if my approach and answer are correct?