Question

Out of 100 persons in a group, 72 persons speak English and 43 persons speak French.
Each one cut of 100 persons speak at least one language. Then how many speak only
English ? How many speak only French ? How many of them speak English and French
both ?



please tell in detail ​

Answer 1

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.

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Answer 2

English 72 French 43)+':"(*"'$;$?6$&'$!$)$8$453)_&9