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.

Question

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?

Answer 1

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.

Answer 2

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