Step-by-step explanation:
We let A be the set of those who owned an iPhone, B be the set of those who owned a Blackberry,
and C those that owned an Android. Therefore we have |A| = 60, |B| = 75, and |C| = 30. Also,
we know that |A ∩ B| = 40, |A ∩ C| = 12 and |B ∩ C| = 8. Finally, |A ∩ B ∩ C| = 3. Therefore,
by the principle of inclusion/exclusion, we have
|A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|
= 60 + 75 + 30 − 40 − 12 − 8 + 4
= 109
(a) Since there are 300 total people, there are 191 without one of the types of phone.
(b) Since |A ∩ B| = 40 and |B| = 75, there are 35 people with a Blackberry that don’t own
an iPhone.
(c) Since |B ∩ C| = 8 and |B| = 75, there are 67 people with a Blackberry that don’t own
an Android.
It is also helpful to draw Venn diagrams for this problem.
