A newspaper vendor sells three papers to 135 customers, the papers are the daily times, the observer and the new Nigeria. 70 cus

Question

3 months ago

6

A newspaper vendor sells three papers to 135 customers, the papers are the daily times, the observer and the new Nigeria. 70 cus

tomers buy the daily time, 60 the observer, 50 the new Nigeria, 17 buy both the daily times and the observer, 15 buy both the observer and the new time Nigeria, 16 the daily times and new Nigeria, how many customers brought (1) all the three papers

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-03-05T11:52:37+03:00

Answer:

Three customers purchased all three newspapers.

Step-by-step explanation:

Let D, O, and N stand for the three newspapers.

D = The Daily Times

O = The Observer

N = The New Nigeria.

According to the provided information,

$n(D\cup O\cup N)=135, n(D)=70,n(O)=60,n(N)=50$

$n(D\cap O)=17, n(O\cap N)=15, n(D\cap N)=16$

We can deduce that:

$n(A\cup B\cup C) = n(A) + n(B) + n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A) + n(A\cap B\cap C)$

Applying this formula, we discover

$n(D\cup O\cup N) = n(D)+n(O) + n(N)-n(D\cap O)-n(O\cap N)-n(N\cap D) + n(D\cap O\cap N)$

$135 =70+60+50-17-15-16 +n(D\cap O\cap N)$

$135 =132+n(D\cap O\cap N)$

$135 -132=n(D\cap O\cap N)$

$3=n(D\cap O\cap N)$

Hence, three customers bought all three papers.