Answer to Question #138760 in Algebra for Cameron Foster

Question

forty-five students in a music appreciation class could attend a piano recital or a voice recital for extra

points. Twenty students attended the piano recital, 23 attended the voice recital, and 10 attended neither.

(a) Please show a Venn Diagram representing the information.

(b) How many students.. .

i. attended both the piano recital and voice recital?

ii. attended only the piano recital?

iii. attended only the voice recital?

iv. attended one or the other, but not both

Answer 1

a. V$\bigcap$ P = V + P - V$\bigcup$ P

= 23+20-35

= 8

Else elements are calculated using this intersection value.

Venn Diagram is shown below-

(b).(i). Number of students who attended both Piano and Voice Recital= 8

(ii). Number of students who attended only Piano Recital = 12

(iii). Number of students who attended only Voice Recital = 15

(iv). Number of students who attended one or the other but not both = 12+15= 27