Question

Ans.
3.
Out of 100 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 ?
kina Fnglish and French respectively​

Answer 1

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• 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.

∴ Number of people speaking French only are 28.

Answer 2

Step-by-step explanation:

english=67

french=28

both=15