Answer to Question #279378 in Discrete Mathematics for Jaishree

Question #279378

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.

1
Expert's answer
2021-12-20T16:22:54-0500
N(PB)=N(P)+N(B)N(PB)N(P\cup B)=N(P)+N(B)-N(P\cap B)

(a)

N(PB)=30+1432=12N(P\cap B)=30+14-32=12

(b)

N(only P)=N(P)N(PB)=3012=18N(only\ P)=N(P)-N(P\cap B)=30-12=18

(c)

N(only B)=N(B)N(PB)=1412=2N(only\ B)=N(B)-N(P\cap B)=14-12=2


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