Question

A survey of 108 college students was taken to determine the musical styles they liked. Of those, 42 students listened to rock, 42 to classical, and 44 to jazz. Also, 25 students listened to rock and jazz, 20 to rock and classical, and 19 to classical and jazz. Finally, 12 students listened to all three musical styles. Construct a Venn diagram and determine the cardinality for each region in order to answer the following question.

How many students listened to music in exactly one of the musical styles?

Answer 1

i just had to do these haha ill help, one sec

Answer 2

n(u) = 108
n(r)=42
n(c)= 42
n(j)=44

n(r intersect j) = 25
n(r intersect c) = 20
n( c intersect j) = 19
n(r intersect j intersect c) = 12

Answer 3

now that we have this information, we start with the inner flower of the venn diagram (what all the similarities are). always try to work from the inside to outside the venn diagram

Answer 4

we start where all 3 intersect, which is 12

Answer 5

next, we see that c intersects j with 19 elements. we have already accounted for 12, so we subtract that 12 from the 19 elements and get 7

Answer 6

next we see that r intersects c with 20 elements. once again, we have already accounted for 12 of those elements, so we subtracts 12 from 20 and get 8.