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in Sets, Relations and Functions by (28.9k points)
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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.

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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

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