Question

in a party of 45 people each one likes tea or coffee or both 35 people like tea and 20 people like cofee . find the number of people who do not like tea​

Answer 1

Answer:

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.

Step-by-step explanation: