Question

Out of 100 persons in a group. 72 persons speaks
French. Each one out of 100 persons speall at least
one of the languagethen how many speak only
English? How many speak only
bench ? How m
many
of them speaks Englisha and French both?​

Answer 1

Answer:

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.please follow me