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.

$\therefore n\left(F\right)=50,n\left(S\right)=20,n(S\cap F)=10$

We know that:
$n(S\cup F)=n\left(S\right)+n\left(F\right)-n(S\cap F)$
$=20+50-10$
$=70-10=60$

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