help trying to figure out what to substract/add

64 students in a classical music lecture class were  polled

 

with the results that

37 like Wolfgang Amadeus  Mozart,

36 like Ludwig von  Beethoven,

30 like Franz Joseph  Haydn,

14 like Mozart and  Beethoven,

21 like Mozart and  Haydn,

14 like Beethoven and  Haydn, and

8 like all three composers

 

 

Let M be the set of students that like  Mozart, B be the set of students that like  Beethoven, and H be the set of students that like Haydn.

 

Venn Diagram. 

 

I like examples because examples have me understand better such as 

25 + 16 = 41

41 - 32 =9

A = 25 - 9 = 16

B = 16 - 9 = 7

 

U = 13 - 7 = 6

 

or examples: 

 

 

(a) 8 Juniors 

(b) 8 seniors

(c) 8 seniors + 12 = 20 

(d) guards or centers 

8 + 3 + 4 + 4 + 1 = 16 

(e) seniors who are not center or college students who are not guards

4 + 8 + 9 + 1 = 22

(f) junior high seniors  who are are not centers 

8 + 5 = 13