Solution: 2019 Winter Midterm - 5
Author: Michiel SmidQuestion
In a group of 100 students,
- 37 students like beer,
- 18 students like cider,
- 55 students do not like beer and do not like cider.
(a)
8
(b)
11
(c)
10
(d)
9
Solution
A = Like beer
$ |A| = 37 $
B = Like cider
$ |B| = 18 $
$ |\overline{A \cup B}| = 55 $
$ |A \cup B| = 100-55 $
$ |A \cup B| = 45 $
$ |A \cap B| = |A| + |B| - |A \cup B| $
$ |A \cap B| = 37 + 18 - 45 $
$ |A \cap B| = 10 $