Question

In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. find the number of people who (i) like both tea and coffee. (iii) do not like coffee. 8. (ii) do not like tea.

Answer 1

Let the set of people who drink tea be T
and the set of people who drink coffee be C
We have all people either drinking one of the 2, so we can write
n(T∪C) = 45 i.e 45 people either drink tea or coffee
and we also have
(i) n(T) = 35

n(C) = 20
We have formula 
n(T∪C) = n(T) + n(C) - n(T∩C)
45 = 35 + 20 - n(T∩C)
n(T∩C) = 55 - 45 = 10 i.e 10 people like both tea and coffee 
(ii) People who dont like coffee will be the part of set T and excluding the part of intersection of T and C, so we have
n(T) - n(T∩C) = people who dont like coffee

35 - 10 = 25

Therefore, 25 people dont like coffee
(iii) Similarly, People who dont like tea will be the part of set C and excluding the part of intersection of T and C, so we have
n(C) - n(T∩C) = people who dont like tea

20 - 10 = 10
Therefore, 10 people dont like tea.

Answer 2

25 is the answer follow me to get answer