Question

In a survey it was found that 21 persons 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

a) The number of people who liked at least one product​

Answer 1

64

Explanation:

To find the number of people who liked at least one product, we need to calculate the total number of unique individuals who liked any of the three products.

We can use the principle of inclusion-exclusion to solve this problem. The principle states that:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Given:

|A| = 21 (number of people who liked product A)

|B| = 26 (number of people who liked product B)

|C| = 29 (number of people who liked product C)

|A ∩ B| = 14 (number of people who liked products A and B)

|A ∩ C| = 12 (number of people who liked products A and C)

|B ∩ C| = 14 (number of people who liked products B and C)

|A ∩ B ∩ C| = 8 (number of people who liked all three products)

Using the formula, we can calculate the number of people who liked at least one product:

|A ∪ B ∪ C| = 21 + 26 + 29 - 14 - 12 - 14 + 8

= 64

Therefore, the number of people who liked at least one product is 64.