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)

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