Question

In a survey of 300 house wires. It was discovered

that 150 had read magazine A, 200 had
read Magazine B and 156 had read
magazine C It was further discovered
that 48 had read A and B 60 had
read B and a while 52 hand read
A and a . Find
The number of housewives that had read.
all three magazine
​

Answer 1

46 housewives read all three magazines.

Explanation:

Answer 2

46 housewives read all three magazines.

Explanation:

Given:

n(A) = 150

n(B) = 200

n(C) = 156

n(A∩B) = 48

n(B∩C) = 60

n(A∩C) = 52

n(A∪B∪C) = 300

so we know the relation as:

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)

∴ n(A∩B∩C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) - n(A∪B∪C)

= 150 + 200+ 156 - 48 - 60 - 52 - 300

= 46

Hence the number of housewives that had read all three magazine is 46.