Question

28 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 magazines A and C, 5 read magazines B and C and 3 read all three
magazines. Find:
a) How many read none of three magazines?
b) How many read magazine C only?​

Answer 1

Answer:

Step-by-step explanation:

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

Mark this ans as brainliest plz