Question

There are 100 people in a group. In this group, 23 people speak English, 26 people speak Telugu, 30 people speak Hindi. And 7 people speak both English and Telugu, 8 people speak English and Hindi and 10 people speak Telugu and Hindi. And 3 people speak all the three languages. Find how many people do not speak any language.

Answer 1

Answer:

Step-by-step explanation:

Let A→ Set of people who speak English.

B→ Set of people who speak French.

A−B→ Set of people who speak English and not French.

B−A→ Set of people who speak French and not English.

A∩B→ Set of people who speak both English and French.

Given  

n(A)=72n(B)=43n(A∪B)=100

Now,

n(A∪B)=n(A)+n(B)−n(A∪B)

                 =72+43−100

                 =15

∴ Number of persons who speak both English and French are 15

n(A)=n(A−B)+n(A∩B)

⇒n(A−B)=n(A)−n(A∩B)

                       =72−15

                       =57

And  

⇒n(B−A)=n(B)−n(A∩B)

                       =43−15

                       =28

∴ Number of people speaking English only are 57.

and Number of people speaking French only are 28.