1. **State the problem:** We have 50 people in total. Among them, 27 know Chinese, 19 know English, and 13 know neither language. We need to find how many people know both Chinese and English. 2. **Define variables:** Let $C$ be the set of people who know Chinese, $E$ be the set of people who know English, and $N$ be the set of people who know neither. 3. **Use the total population:** Total people $= 50$ 4. **People who know at least one language:** Since 13 know neither, the number who know at least one language is $$50 - 13 = 37$$ 5. **Use the formula for union of two sets:** $$|C \cup E| = |C| + |E| - |C \cap E|$$ We know $|C \cup E| = 37$, $|C| = 27$, and $|E| = 19$. 6. **Solve for $|C \cap E|$:** $$37 = 27 + 19 - |C \cap E|$$ $$|C \cap E| = 27 + 19 - 37 = 46 - 37 = 9$$ 7. **Answer:** 9 people know both Chinese and English.