Out of 100 persons in a group, 72 persons Speak
French Each one out of 100 persons speak at least and
language. Then how many speak only english? How
many at them speak English ard french both?
pls explain in steps
thank you.
Answers
Answer:
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.
Step-by-step explanation:
Step-by-step explanation:
n(a u b) = 100 = total no. of people
n(a) = 72 = no of people speak French
n(b)= 43
n(a) + n(b) = n(a u b) + n(a ū b)
72 + 43 = 100 + n(a ū b)
115- 100 = n(a ū b)
n(a ū b) = 15 = no. of people who speak both
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