Question

In a group of 26 persons 8 take tea but not coffee and 16 take tea. How many of them take coffee but not tea?

Answer 1

Hint: Venn Diagram: Venn diagram is a technique that uses circles to show the relationship between the events that which event is included or not. With these Venn diagrams, events can be calculated easily. Here \[n(A \cup B) = n(A) + n(B) - n(A \cap B)\].
Where \[n(A \cup B)\] is the number of the event which is the union of \[A\& B\] and \[n(A \cap B)\] is the number of events which is the intersection of \[A\& B\].

Complete step-by-step answer:

Given, total persons = 26.

Let us denote the person who drinks tea as ‘T’ and who drinks coffee as ‘C’. Also (T-C) be the persons who take tea but not coffee and (C-T) be those who take coffee but not tea.

Given, $n(T) = 16$

$n(T \cup C) = 16$
$n(T - C) = 8$
$n(T) = 16$
To find $n(C - T) = ?$
$n(T - C) = 8$
$n(T) = 16$
$n(C - T) = ?$

Here, $n(C - T) = n(C \cup T) - n(T)$
=$26 - 16$
=$10$

Therefore 10 people take coffee but not tea.

Note: 1) Union is the collection of all events except repetition.
2) Intersection is the only repeated or the same events in the events.
3) Subset is that which is taken from the set. Here B is the proper subset of A which is taken from A.
4) n (A – B) is the number of events where A went is happening but B is not.