In a group of 50 persons, 30 like tea, 25 like coffee and 16 like both. How many like
(i) either tea or coffee?
(ii) neither tea nor coffee?
Given:
In a group of 50 persons,
-30 like tea
-25 like coffee
-16 like both tea and coffee
To find:
(i) People who like either tea or coffee.
Let us consider
Total number of people = n(X) = 50
People who like tea = n(T) = 30
People who like coffee = n(C) = 25
People who like both tea and coffee $=n(T \cap C)=16$
People who like either tea or coffee $=n(T \cup C)$
Venn diagram:
Therefore,
$n(T \cup C)=n(T)+n(C)-n(T \cap C)$
$=30+25-16$
$=39$
Thus, People who like either tea or coffee = 39
(ii) People who like neither tea nor coffee.
People who like neither tea nor coffee $=n(X)-n(T \cup C)$
$=50-39$
$=11$
Therefore, People who like neither tea nor coffee = 11