Question

Steve is a fan of the music of Paul Simon and Art Garfunkel. In his collection of 25 compact discs, he has the following:

5 on which both Simon and Garfunkel sing

7 on which Simon sings

8 on which Garfunkel sings

15 on which neither Simon nor Garfunkel sings

a) How many of his compact discs feature only Paul Simon?

b) How many of his compact discs feature only Art Garfunkel?

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

Answer 1

a) 2

b) 3

c) 10

Explanation:

Let U represent the universal set of all compact discs Steve has in his collection

let S represent the set of compact discs on which Simon sings and

let G represent the set of compact discs on which Garfunkel sings

⇒Given data can now be represented as:

• n(U) = 25
• n(S∩G) = 5
• n(S) = 7
• n(G) = 8
• n((S∪G)') = 15 (where A' represents complement of set A)

a)

n(S-G) = n(S) - n(S∩G) = 7-5 = 2

b)

n(G-S) = n(G) - n(S∩G) = 8-5 = 3

c)

number of compact discs featuring at least one of the two artists = total number of compact discs - the number of compact discs not featuring any of the artists = n(U) - n((S∪G)') = 25 - 15 = 10