In a survey, 175 consumers were asked about their buying preferences concerning a product that is sold in the market under three labels. The results were as follows.

14 buy only those sold under label A.
25 buy only those sold under label B.
28 buy only those sold under label C.
14 buy only those sold under labels A and B.
10 buy only those sold under labels A and C.
15 buy only those sold under labels B and C.
9 buy the product sold under all three labels.

How many of the consumers surveyed buy the product sold under
(a) At least one of the three labels?
(b) Labels A and B but not C?
(c) Label A?
(d) None of these labels?

Draw a Venn diagram with three overlapping circles A, B and C.

Hint:
start with the area A∩B∩C (in the middle) and work outwards.

When completed, it will be a snap to answer the given questions.

In a survey, 175 consumers were asked about their buying preferences concerning a product that is sold in the market under three labels. The results were as follows.

15 buy only those sold under label A.
25 buy only those sold under label B.
28 buy only those sold under label C.
13 buy only those sold under labels A and B.
9 buy only those sold under labels A and C.
11 buy only those sold under labels B and C.
10 buy the product sold under all three labels.
How many of the consumers surveyed buy the product sold under

(a) At least one of the three labels: Well, let's do some calculations. If we add up the number of people who buy the product sold under label A (14), label B (25), label C (28), and those who buy under multiple labels (14+10+15+9), we get a total of 90. So, 90 consumers surveyed buy the product sold under at least one of the three labels.

(b) Labels A and B but not C: According to the information given, 14 consumers buy only those sold under labels A and B. So, 14 consumers surveyed buy the product sold under labels A and B but not under label C.

(c) Label A: Looking at the information provided, if we add up the number of people who buy the product sold under label A only (14), who buy it under labels A and B (14), and who buy it under labels A and C (10), we get a total of 38. Hence, 38 consumers surveyed buy the product sold under label A.

(d) None of these labels: To find the number of consumers surveyed who do not buy the product sold under any of these labels, we need to subtract the total number of consumers mentioned in the previous answers from the total number of consumers surveyed.

Total consumers surveyed = 175.
Consumers who buy under at least one label (90) + Consumers who buy under labels A and B but not C (14) + Consumers who buy under label A (38) = 142.

So, the number of consumers surveyed who do not buy the product sold under any of these labels is 175 - 142 = 33.

I hope these answers satisfy your curiosity! If not, I can always try juggling the numbers to make it more entertaining. 🤡

To find the number of consumers who buy the product under different conditions, we need to use the principles of set theory.

(a) To determine the number of consumers who buy the product under at least one label, we need to add up the number of consumers who buy under each individual label and subtract the duplicates.

In this case, using the information provided, we can calculate it as follows:

14 (buy only A) + 25 (buy only B) + 28 (buy only C) + 14 (buy A and B) + 10 (buy A and C) + 15 (buy B and C) + 9 (buy all three labels) = 105

So, 105 consumers buy the product sold under at least one label.

(b) To find the number of consumers who buy the product under labels A and B but not C, we need to subtract the number of consumers who buy under all three labels.

In this case, based on the information given:

14 (buy A and B) - 9 (buy all three labels) = 5

So, 5 consumers buy the product under labels A and B but not C.

(c) To determine the number of consumers who buy the product under label A, we need to add up the consumers who buy only A and those who buy A along with other labels.

In this case, based on the information given:

14 (buy only A) + 14 (buy A and B) + 10 (buy A and C) + 9 (buy all three labels) = 47

So, 47 consumers buy the product under label A.

(d) To find the number of consumers who do not buy the product under any of the three labels, we subtract the total number of consumers from the number of consumers who buy under at least one label.

In this case:

175 (total surveyed) - 105 (buy at least one label) = 70

So, 70 consumers do not buy the product under any of the three labels.

To summarize:
(a) At least one of the three labels: 105
(b) Labels A and B but not C: 5
(c) Label A: 47
(d) None of these labels: 70