Question

(3)
Out of 100 persons in a group, 72 persons speak English and 43 perseus speak French.
Each one out 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?​

Answer 1

Step-by-step explanation:

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.

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Answer 2

Let U be the set of all the persons, E be the set of persons who speak English,  F be the set of persons who speak French and x people speak both the languages.

Since, each one out of 100 persons speak at least one language.  

∴ n(U) = n(E ∪ F) = 100  

∴ 72 – x + x + 43 – x = 100  ∴ 115 – x = 100  

∴ x = 115 – 100 = 15.

Number of people who speak English and French = 15

Number of people who speak only English = 72 – x = 72 – 15 = 57

Number of people who speak only French = 43 – x = 43 – 15 = 28

   

                      Hope it was helpful!!!!!!