Question

Out of hundred persons in a group, 72 persons speak English and 43 persons 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

❤$\huge\mathbb{\underline{\underline{Question:-}}}$

⭐Out of hundred persons in a group, 72 persons speak English and 43 persons 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?

✒$\huge\mathbb{\underline{\underline{Solution:-}}}$

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

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