Question:
In a survey of 100 persons it was found that 28 read magazine A, 30
read magazine B, 42 read magazine C, 8 read magazines A & B, 10
read magazine B&C and 3 read all the three. Find:
i) How many read none of the magazines?
ii) How many read magazine C only?
iii) How many read magazine A only?
iv) How many read magazine B & C but not A ?
Answer:
The correct question is:
In a survey of 100 persons, it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A and B, 10 read magazine A and C, 5 read magazine B and C and 3 read all the three. Find: i) How many read none of the magazines? ii) How many read magazine C only? iii) How many read magazine A only? iv) How many read magazine B & C but not A?
Solution:
Let A: Set of persons who read magazine A
B: Set of persons who read magazine B
C: Set of persons who read magazine C
Given, Total person N = 100
n(A) = 28, n(B) = 30, n(C) = 42,
n(A ∩ B) = 8, n(A ∩ C) = 10, n(B ∩ C) = 5,
n(A ∩ B ∩ C) = 3
1. Number of students who read none of the magazine = n(A ∪ B ∪ C)
= n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
= 28 + 30 + 42 - 8 - 10 - 5 + 3
= 103 - 23
= 80
2. Number of students who read the magazine C only = n(C) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
= 42 - 10 - 5 + 3
= 45 - 15
= 30
3. Number of students who read the magazine A only = n(A) - n(A ∩ C) - n(A ∩ B) + n(A ∩ B ∩ C)
= 28 - 10 - 8 + 3
= 31 - 18
= 13
4. Number of students who read the magazine B and C but not A = n((B ∩ C) - A)
= n(B ∩ C) - n(A ∩ B ∩ C)
= 5 - 3
= 2
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