To find the answers to these questions, we can use a Venn diagram.
First, let's draw a Venn diagram with three circles representing the types of books: mysteries, science fiction, and romance novels.
a) To find how many customers purchased only mysteries, we need to count the number of customers in the mysteries circle who are not in any other circles. From the given information, we know that 18 customers purchased mysteries and science fiction, 12 purchased mysteries and romance novels, and 3 purchased all three types of books. So, 18 + 12 + 3 = 33 customers purchased mysteries in total. Since the total number of customers surveyed is 70, subtracting 33 from 70 gives us the number of customers who purchased only mysteries: 70 - 33 = 37 customers.
b) To find how many customers purchased mysteries and science fiction but not romance novels, we need to look at the intersection of the mysteries and science fiction circles. From the given information, we know that 18 customers purchased mysteries and science fiction. To exclude those who also purchased romance novels, we subtract the 3 customers who purchased all three types of books. So, 18 - 3 = 15 customers purchased mysteries and science fiction but not romance novels.
c) To find how many customers purchased mysteries or science, we need to count the total number of customers in the mysteries and science fiction circles together. From the given information, we know that 18 customers purchased mysteries and science fiction, but we don't know how many customers purchased only science fiction. So, we need to calculate the number of customers who purchased only science fiction. To do this, subtract the 15 customers who purchased mysteries and science fiction but not romance novels from the total number of customers who purchased science fiction: 34 - 15 = 19. Finally, add the 18 customers who purchased mysteries and science fiction to the 19 customers who purchased only science fiction: 18 + 19 = 37 customers who purchased mysteries or science.
d) To find how many customers purchased mysteries or science fiction but not romance novels, we need to count the total number of customers in the mysteries and science fiction circles but exclude the overlap with the romance novels circle. From the given information, we know that 18 customers purchased mysteries and science fiction, and 9 purchased science fiction and romance novels. We also know that 3 customers purchased all three types of books. To find the number of customers who purchased mysteries or science fiction but not romance novels, we add the customers who purchased only mysteries (37) to the customers who purchased only science fiction (19), and subtract the customers who purchased all three types of books (3): 37 + 19 - 3 = 53 customers.
e) To find the number of customers who purchased exactly two types of books, we need to count the total number of customers in the overlapping regions of the Venn diagram. From the given information, we know that 3 customers purchased all three types of books. To find the number of customers who purchased exactly two types, we add the number of customers who purchased mysteries and science fiction (18) to the number of customers who purchased mysteries and romance novels (12) to the number of customers who purchased science fiction and romance novels (9), and subtract the customers who purchased all three types (3): 18 + 12 + 9 - 3 = 36 customers.