Answer to Question #279378 in Discrete Mathematics for Jaishree

Question

Suppose among 32 people who save paper or bottles (or both) for recycling,

there are 30 who save paper and 14 who save bottles. Find the number m of

people who:

(a) save both; (b) save only paper; (c) save only bottles.

Answer 1

$$N(P\cup B)=N(P)+N(B)-N(P\cap B)$$

(a)

$$N(P\cap B)=30+14-32=12$$

(b)

$$N(only\ P)=N(P)-N(P\cap B)=30-12=18$$

(c)

$$N(only\ B)=N(B)-N(P\cap B)=14-12=2$$