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 ?
Answers
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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