To solve this problem, we can use a method called Venn diagrams. Venn diagrams are a graphical representation of the relationships between different sets or groups of things. In this case, we will use a Venn diagram to represent the three types of books: mysteries, science fiction, and romance novels.
Step 1: Draw three overlapping circles to represent the three types of books: mysteries, science fiction, and romance novels. Label each circle accordingly.
Step 2: Fill in the information given in the problem. We know that 36 customers purchased mysteries, 28 purchased science fiction, and 21 purchased romance novels. Place these numbers in the respective circles.
Step 3: Next, place the additional information provided. 15 customers purchased both mysteries and science fiction, 12 purchased both mysteries and romance novels, and 8 purchased both science fiction and romance novels. Additionally, 4 customers purchased all three types of books. Fill in these numbers accordingly.
Step 4: Add up the numbers in each section of the Venn diagram to get the total number of customers in each category.
According to the information given, the Venn diagram would look like this:
Mysteries (36)
_______
| |
| 4 | Science Fiction (28)
| |
|_______|
Romance Novels (21)
Step 5: Analyze the Venn diagram to get the answer to the question.
a) To find the number of customers who purchased only mysteries, add up the numbers in the region that belongs only to the mysteries circle. In this case, it is the 36 customers who purchased mysteries minus the 15 who also purchased science fiction and the 12 who also purchased romance novels. So, the answer is 36 - 15 - 12 = 9.
b) To find the number of customers who purchased only science fiction, do the same in the science fiction circle. It is the 28 customers who purchased science fiction minus the 15 who also purchased mysteries and the 8 who also purchased romance novels. So, the answer is 28 - 15 - 8 = 5.
c) To find the number of customers who purchased only romance novels, do the same in the romance novels circle. It is the 21 customers who purchased romance novels minus the 12 who also purchased mysteries and the 8 who also purchased science fiction. So, the answer is 21 - 12 - 8 = 1.
d) To find the number of customers who did not purchase any of the three types of books, add up the numbers in the region outside all three circles. In this case, it is the total number of customers surveyed (59) minus the sum of all the numbers inside the Venn diagram (36 + 28 + 21 - 15 - 12 - 8 + 4). So, the answer is 59 - (36 + 28 + 21 - 15 - 12 - 8 + 4) = 59 - 74 = -15. Since having a negative number of customers doesn't make sense, we can conclude that there might be a mistake in the provided information or the Venn diagram.
The Venn diagram method allows us to visualize and solve problems involving overlapping sets, providing a clear understanding of the relationships between different groups.