Try this beautiful problem from B.Math Entrance Exam based on Sets and Venn diagrams.
In a village of 1000 inhabitants, there are three newspapers P, Q,and R in circulation. Each of these papers is read by 500 persons. Papers P and Q are read by 250 persons, papers Q and R are read by 250 persons, papers R and P are read by 250 persons.All the three papers are read by 250 persons. Then the number of persons who read no newspaper at all
Sets
Venn diagrams
Algebra
Answer: is 0.
B. Math Entrance, India
Test of Mathematics at 10+2 Level by East West Press
Here n(P)=500, n(Q)=500, n(R)=500, n(PQ)=250, n(QR)=250, n(RP)=250, n(PQR)=250
n(P+Q+R)=n(P)+n(Q)+n(R)-n(PQ)-n(QR)-n(RP)+n(PQR)
n(P+Q+R)=1000 Then P,Q and R read by 1000 inhabitantsand the number of persons who read no newspaper at all is 0.
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