Question

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 1

Let F be the set of people in the committee who speak French, 

and S be the set of people in the committee who speak Spanish 

∴ n(F) = 50, n(S) = 20, n(S ∩ F) = 10 

We know that:

 n(S ∪ F) = n(S) + n(F) – n(S ∩ F) 

= 20 + 50 – 10 

= 70 – 10 = 60 

Thus, 60 people in the committee speak at least one of the two languages.