In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Answer
Let F and F represent the set of people in the committee who speak Spanish and French respectively.
Given that n(F) = 50, n(S) = 20 and n(S ∩ F) = 10
Use the formula:
n(S ∪ F) = n(S) + n(F) - n(S ∩ F)
Plug the values, we get
⇒ 20 + 50 - 10
⇒ 70 - 10
⇒ 60
Hence, 60 people in the committee speak at least one of these two languages.