Let N= National savings certificates S= Shares Total no. of persons =32 No. of persons who invest in National savings certificates =30 No. of persons who invest in shares =17 Therefore n(N∪S)=32,n(N)=30,n(S)=17 We know that, n(N∪S)=n(N)+n(S)−n(N∩S) ⇒ 32=30+17−n(N∩S) ⇒ n(N∩S)=47−32=15