In a survey it was found that 21 persons liked product P 1 , 26 liked product P 2 and 29 liked product P 3 . If 14 persons liked products P 1 and P 2 ; 12 persons liked product P 3 and P 1 ; 14 persons liked products P 2, and P 3 and 8 liked all the three products. Find how many liked product P 3 only.

Question

Philoid · Accepted Answer

Let n(P₁) be a number of people liking product P₁.

Let n(P₂) be a number of people liking product P₂.

Let n(P₃) be a number of people liking product P₃.

Then, According to the question:

n(P₁) = 21, n(P₂) = 26, n(P₃) = 29, n(P₁∩ P₂) = 14

n(P₁∩ P₃) = 12, n(P₂∩ P₃) = 14, n(P₁∩ P₂ ∩ P₃) = 8.

∴ Number of people liking product P₃ only:

= 29–(4+8+6)

= 29– 18

=11

In a survey it was found that 21 persons liked product P1, 26 liked product P2 and 29 liked product P3. If 14 persons liked products P1 and P2; 12 persons liked product P3 and P1; 14 persons liked products P2, and P3 and 8 liked all the three products. Find how many liked product P3 only.