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.

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.