Question

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Answer 1

Let, X , Y and Z be the number of people who like product A, product B and product C respectively.

Therefore, n( X )=21

n( Y )=26

n( Z )=29

n( X∩Y )=14

n( Z∩X )=12

n( Y∩Z )=14

n( X∩Y∩Z )=8

Number of people who liked product C​ only = n( Z )−n( X∩Z )−n( Y∩Z )+n( X∩Y∩Z ) =29−12−14+8 =11

Hence, the number of people who like product C only is 11 .