1. **Stating the problem:** We have 80 students in year 11. - 9 students study both French and German. - 35 students study only French. - 2 students do not study French or German. We need to complete the Venn diagram and find how many students study only German. 2. **Understanding the sets:** Let: - $F$ = set of students studying French - $G$ = set of students studying German - $F \cap G$ = students studying both French and German = 9 - $F \setminus G$ = students studying only French = 35 - Students not studying French or German = 2 3. **Total students:** Total students = 80 4. **Calculate students studying German only:** The total students can be expressed as: $$|F \setminus G| + |G \setminus F| + |F \cap G| + \text{neither} = 80$$ Substitute known values: $$35 + |G \setminus F| + 9 + 2 = 80$$ Simplify: $$35 + |G \setminus F| + 11 = 80$$ $$|G \setminus F| + 46 = 80$$ Subtract 46 from both sides: $$|G \setminus F| = 80 - 46$$ $$|G \setminus F| = 34$$ 5. **Answer:** The number of students who study only German is **34**. 6. **Summary:** - Only French: 35 - Only German: 34 - Both French and German: 9 - Neither: 2 This completes the Venn diagram.