Respuesta :
Treating the events as Venn events, it is found that:
a) 13 customers purchased only mysteries.
b) 27 customers purchased mysteries and science fiction, but not romance novels.
c) 53 customers purchased mysteries or science fiction.
d) 36 customers purchased mysteries or science fiction, but not romance novels.
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We consider:
- Event A: Purchased mysteries.
- Event B: Purchased science fiction.
- Event C: purchased romance.
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4 purchased all three types of books, thus:
[tex](A \cap B \cap C) = 4[/tex]
8 purchased science fiction and romance novels, thus:
[tex](B \cap C) + (A \cap B \cap C) = 8[/tex]
[tex](B \cap C) = 4[/tex]
13 purchased mysteries and romance novels:
[tex](A \cap C) + (A \cap B \cap C) = 13[/tex]
[tex](A \cap C) = 9[/tex]
18 purchased mysteries and science fiction:
[tex](A \cap B) + (A \cap B \cap C) = 14[/tex]
[tex](A \cap B) = 14[/tex]
22 purchased romance novels:
[tex]C + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 22[/tex]
[tex]C + 9 + 4 + 4 = 22[/tex]
[tex]C = 5[/tex]
31 purchased science fiction:
[tex]B + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 31[/tex]
[tex]B + 14 + 4 + 4 = 31[/tex]
[tex]B = 9[/tex]
40 customers purchased mysteries:
[tex]A + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 40[/tex]
[tex]A + 14 + 9 + 4 = 40[/tex]
[tex]A = 13[/tex]
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Item a:
Only mysteries is A, which is 13.
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Item b:
This is:
[tex]A - C = A + (A \cap B) = 13 + 14 = 27[/tex]
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Item c:
This is:
[tex]A \cup B = A + B + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 13 + 9 + 14 + 9 + 4 + 4 = 53[/tex]
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Item d:
This is:
[tex](A \cup B) - C = A + B + (A \cap B) = 13 + 9 + 14 = 36[/tex]
A similar problem is given at https://brainly.com/question/21421475
