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

46 housewives read all three magazines.

Step-by-step 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.