Answer:
Step-by-step explanation: a) To find out how many customers purchased only romance novels, we need to subtract the customers who purchased romance novels and another genre(s) from the total number of customers who purchased romance novels.From the given data, we know that:11 purchased mysteries and romance novels7 purchased science fiction and romance novels3 purchased all three types of booksTherefore, the number of customers who purchased only romance novels is:21 (total purchased romance novels) - 11 (purchased mysteries and romance novels) - 7 (purchased science fiction and romance novels) - 3 (purchased all three types of books) = 21 - 11 - 7 - 3 = 0So, none of the customers surveyed purchased only romance novels.b) To find out how many customers purchased mysteries and science fiction, but not romance novels, we need to subtract the customers who purchased all three types of books and those who purchased mysteries, science fiction, and romance novels from the total number of customers who purchased mysteries and science fiction.From the given data, we know that:14 purchased mysteries and science fiction11 purchased mysteries and romance novels7 purchased science fiction and romance novels3 purchased all three types of booksTherefore, the number of customers who purchased mysteries and science fiction, but not romance novels is:14 (total purchased mysteries and science fiction) - 3 (purchased all three types of books) - 11 (purchased mysteries and romance novels) = 14 - 3 - 11 = 0So, none of the customers surveyed purchased mysteries and science fiction, but not romance novels.c) To find out how many customers purchased mysteries or science fiction, we need to add the customers who purchased only mysteries, only science fiction, and those who purchased both.From the given data, we know that:34 purchased mysteries (including 14 who also purchased science fiction and 11 who also purchased romance novels)27 purchased science fiction (including 14 who also purchased mysteries and 7 who also purchased romance novels)Therefore, the number of customers who purchased mysteries or science fiction is:34 (total purchased mysteries) - 14 (purchased mysteries and science fiction) + 27 (total purchased science fiction) - 14 (purchased mysteries and science fiction) + 14 (purchased mysteries and science fiction) = 47So, 47 of the customers surveyed purchased mysteries or science fiction.d) To find out how many customers purchased mysteries or science fiction, but not romance novels, we need to subtract the customers who purchased mysteries, science fiction, and romance novels from the total number of customers who purchased mysteries or science fiction.From the given data, we know that:14 purchased mysteries and science fiction11 purchased mysteries and romance novels7 purchased science fiction and romance novels3 purchased all three types of booksTherefore, the number of customers who purchased mysteries or science fiction, but not romance novels is:34 (total purchased mysteries) - 11 (purchased mysteries and romance novels) + 27 (total purchased science fiction) - 7 (purchased science fiction and romance novels) - 14 (purchased mysteries and science fiction) - 3 (purchased all three types of books) = 23So, 23 of the customers surveyed purchased mysteries or science fiction, but not romance novels.e) To find out how many customers purchased exactly two types of books, we need to add the customers who purchased only mysteries and science fiction, only mysteries and romance novels, and only science fiction and romance novels.