# 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.

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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