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?
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
$\therefore n(F)=50, n(S)=20, n(S \cap F)=10$
We know that:
$n(S \cup F)=n(S)+n(F)-n(S \cap F)$
$=20+50-10$
$=70-10=60$
Thus, $60$ people in the committee speak at least one of the two languages.
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