Question

HELP QUICK!

Answer 1

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