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64. In a survey it was found that 21 people liked product A, 26 liked product B and29 liked product C. If 14 people liked products A and B, 12 people liked productsC and A, 14 people liked products B and C and 8 liked all the three products.Find how many liked product C only.

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Payal Gupta | Contributor-Level 10

4 months ago

64. Let A, B and C be the set of people who like product A, B and C respectively.

Then,

Number of people who like product A, n (A) = 21

Number of people who like product B, n (B) = 26

Number of people who like product C, n (C) = 29.

Number of people likes both product A and B, n (A $\cap$ B) = 14

Number of people likes both product A and C, n (A $\cap$ C) = 12

Number of people likes both product B and C, n (B $\cap$ C) = 14.

No. of people who likes all product, n (A $\cap$ B $\cap$ C) = 8

a→n (A $\cap$ B)

b→n (A $\cap$ C)

d→n (B $\cap$ C)

c→n (A $\cap$ B $\cap$ C)

From the above venn diagram we can see that,

Number of people who likes product C only

= n (C) - b - d + c

= n (C) - n (A $\cap$ C) - n (B $\cap$ C) + n (A $\cap$ B $\cap$ C)

= 29

...more

64. Let A, B and C be the set of people who like product A, B and C respectively.

Then,

Number of people who like product A, n (A) = 21

Number of people who like product B, n (B) = 26

Number of people who like product C, n (C) = 29.

Number of people likes both product A and B, n (A $\cap$ B) = 14

Number of people likes both product A and C, n (A $\cap$ C) = 12

Number of people likes both product B and C, n (B $\cap$ C) = 14.

No. of people who likes all product, n (A $\cap$ B $\cap$ C) = 8

a→n (A $\cap$ B)

b→n (A $\cap$ C)

d→n (B $\cap$ C)

c→n (A $\cap$ B $\cap$ C)

From the above venn diagram we can see that,

Number of people who likes product C only

= n (C) - b - d + c

= n (C) - n (A $\cap$ C) - n (B $\cap$ C) + n (A $\cap$ B $\cap$ C)

= 29 - 12 - 14 + 8

= 11

less

64. Let A, B and C be the set of people who like product A, B and C respectively.Then, Number of people who like product A, n (A) = 21Number of people who like product B, n (B) = 26Number of people who like product C, n (C) = 29.Number of people likes both product A and B, n (A<math><mrow><mo>∩</mo></mrow></math>B) = 14Number of people likes both product A and C, n (A<math><mrow><mo>∩</mo></mrow></math>C) = 12Number of people likes both product B and C, n (B<math><mrow><mo>∩</mo></mrow></math>C) = 14.No. of people who likes all product, n (A<math><mrow><mo>∩</mo></mrow></math>B<math><mrow><mo>∩</mo></mrow></math>C) = 8<div><div><picture><img src="https://images.shiksha.com/mediadata/images/articles/1729492136php63i1N8.jpeg" alt="" width="221" height="227"></picture></div><div>a→n (A<math><mrow><mo>∩</mo></mrow></math>B)b→n (A<math><mrow><mo>∩</mo></mrow></math>C)d→n (B<math><mrow><mo>∩</mo></mrow></math>C)c→n (A<math><mrow><mo>∩</mo></mrow></math>B<math><mrow><mo>∩</mo></mrow></math>C)From the above venn diagram we can see that, Number of people who likes product C only= n (C) - b - d + c= n (C) - n (A<math><mrow><mo>∩</mo></mrow></math>C) - n (B<math><mrow><mo>∩</mo></mrow></math>C) + n (A<math><mrow><mo>∩</mo></mrow></math>B<math><mrow><mo>∩</mo></mrow></math>C)= 29 - 12 - 14 + 8= 11</div></div>

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64. In a survey it was found that 21 people liked product A, 26 liked product B and29 liked product C. If 14 people liked products A and B, 12 people liked productsC and A, 14 people liked products B and C and 8 liked all the three products.Find how many liked product C only.

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