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?

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Solution

Determine the number of students who speak at least one of two languages:
The number of people, who speak French is $F = 50$ .
The number of people, who speak Spanish is $S = 20$ .
The number of people, who speak both French and Spanish is $F \cap S = 10$ .
The number of people, who speak at least one of these two languages can be determined by $F \cup S$ .
$F \cup S = F + S - F \cap S \Rightarrow F \cup S = 50 + 20 - 10 \Rightarrow F \cup S = 60$
Therefore, the number of students, who speak at least one of two languages is $60$ .

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