Venn diagram

Question

Compact Disc Collection Gitti is a fan of the music of Paul Simon and Art Garfunkel.In her collection of 25 compact disc, she has the following:

 

5 on which both Simon and Garfunkel sing

7 on whixh Simon sings

8 on which Garfunkel sings

15 on which neither Simon nor Garfunkel sings.

 

a) How many of her compact disc feature only Paul Simon?

b) How many of her compact discs feauture only Art Garfunkel?

c) How many  feauture at least one of these two artists?

d) How many feature at most one of these two artists.

Answer 1

a) 2

b) 3

c) 10

d) 5

total discs are 25

15 have neither Paul or Art

25-15 = 10 have at least one of Paul or Art = c)

5 have both, 10-5 = 5 have at most one of the two = d)

which also = a) + b) = 2+3 =5

a) = 7-5 = 2

b) = 8-5 = 3

draw two overlapping circles. the overlap = 5

the two circles are inside a rectangle, the area between the circles and the rectangle is 15

the two circles have 10 discs, 5 are the overlap, 5 are just one of each, Art or Paul