In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.
Question 1 Report
In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.
Answer Details
Let F be the set of people who can speak French and E be the set of people who can speak English. Then,
n(F) = 400
n(E) = 350
n(F ∪ E) = 500
We have to find n(F ∩ E).
Now, n(F ∪ E) = n(F) + n(E) – n(F ∩ E)
⇒ 500 = 400 + 350 – n(F ∩ E)
⇒ n(F ∩ E) = 750 – 500 = 250.
∴ 250 people can speak both languages.
n(F) = 400
n(E) = 350
n(F ∪ E) = 500
We have to find n(F ∩ E).
Now, n(F ∪ E) = n(F) + n(E) – n(F ∩ E)
⇒ 500 = 400 + 350 – n(F ∩ E)
⇒ n(F ∩ E) = 750 – 500 = 250.
∴ 250 people can speak both languages.
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