Question

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper 1, 9 read both H and 1, 11 read both H and T, 8 read both T and 1, 3 read all three newspapers. Find: the number of people who read at least one of the newspapers.

Answer 1

Let us assume P is the set of people who read newspaper H.
Also, let Q is the set of people who read newspaper T.
And, let R is the set of people who read newspaper I.

A/C to question,
Number of people who read newspaper H, n(P) = 25
Number of people who read newspaper T, n(Q) = 26
Number of people who read newspaper I, n(R) = 26
Number of people who read both newspaper H and I, n(P ∩ R) = 9
Number of people who read both newspaper H and T, n(P ∩ Q) = 11
Number of people who read both newspaper T and I, n(Q ∩ R) = 8

And, Number of people who read all three newspaper H, T and I, n(P ∩ Q ∩ R) = 3
Now, we have to find number of people who read atleast one of the newspaper , n(P U Q U R)

use formula,
n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C).

so, n(P U Q U R) = n(P) + n(Q) + n(R) - n(P ∩ Q) - n(Q ∩ R) - n(P ∩ R) + n(P ∩ Q ∩ R)

= 25 + 26 + 26 – 11 – 8 – 9 + 3

= 80 – 28

= 52

∴ There are total 52 students who read atleast one newspaper

Answer 2

Answer:

Step-by-step explanation: