Answer: a) The customers surveyed purchased only mysteries =12
b) The customers purchased mysteries and science fiction, but not romance novels=10
c) The customers purchased mysteries or science fiction=46
d) The customers purchased mysteries or science fiction, but not romance novels=44
e) The customers purchased exactly two types of books=21
Step-by-step explanation:
Given: n(S)=57
n(M)=33
n(S)=25
n(R)=18
n(M∩S)=12
n(R∩M)=9
n(S∩R)=6
n(R∩S∩M)=2
From the Venn diagram,
d=2
n(M∩S)=a+d=12
⇒a=10
n(R∩M)=b+d=9
⇒b=7
n(S∩R)=c+d=6
⇒c=4
Now, the customers surveyed purchased only mysteries=n(M)-a-b-d=33-10-7-4=12
The customers purchased mysteries and science fiction, but not romance novels=a=10
The customers purchased mysteries or science fiction=n(M∪S)=n(M)+n(S)-n(M∩S)=33+25-12=46
The customers purchased mysteries or science fiction, but not romance novels=n(M∪S)-d=46-2=44
The customers purchased exactly two types of books= a+b+c=10+7+4=21
