.
In a survey of 600 people in Windhoek, the results of the survey showed that
250 people read The Namibian, 260 people read The Mmegi, and 260 people
read The Daily Mirror. Additionally, 90 people read both The Namibian and The
Daily Mirror, and 110 read both The Namibian and Mmegi, 80 read both The
Mmegi and The Daily Mirror and 80 did not read any of the above newspapers.
Find the number of people who read all the three newspapers.
~~~~~~~~~~~~~~~
If A, B, and C are three subset in an finite universal set U, then
n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C),
where n(X) denotes the number of elements in subset X.
Apply this formula for the given situation. Substitute the given numbers into the formula.
You will get
600 - 80 = 250 + 260 + 260 - 90 - 110 - 80 + n(A ∩ B ∩ C),
or
520 = 490 + n(A ∩ B ∩ C),
which implies
n(A ∩ B ∩ C) = 520 - 490 = 30.
ANSWER. 30 persons read all three newpapers.
Solved.
---------------
To see many other similar solved problems of this kind, look into the lessons
- Counting elements in sub-sets of a given finite set
- Advanced problems on counting elements in sub-sets of a given finite set
- Challenging problems on counting elements in subsets of a given finite set
- Selected problems on counting elements in subsets of a given finite set
in this site.
- - - E N J O Y (!) - - -