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In a committee, 50 people speak French,...

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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To solve the problem, we need to find the number of people who speak at least one of the two languages: French or Spanish. We can use the principle of inclusion-exclusion for this. ### Step-by-Step Solution: 1. **Identify the given values**: - Let \( N_F \) be the number of people who speak French. \( N_F = 50 \) - Let \( N_S \) be the number of people who speak Spanish. \( N_S = 20 \) - Let \( N_{F \cap S} \) be the number of people who speak both languages. \( N_{F \cap S} = 10 \) ...
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