1. **Stating the problem:** We have 25 students studying languages French (F), Spanish (S), and Arabic (A). Some numbers in the Venn diagram are given, and we need to complete it using the information: - Intersection of all three: 1 - Intersection of F and S only: 4 - Intersection of S only: 5 - Intersection of A only: 2 - F only is empty initially - All students who study both Arabic and Spanish also study French - 7 students study French only - 8 students study Arabic total 2. **Understanding the sets and notation:** - Let $x$ be the number of students studying both Arabic and French but not Spanish. - Let $y$ be the number of students studying both Arabic and Spanish but not French. 3. **Using the given info:** - Since all students who study both Arabic and Spanish also study French, the intersection of Arabic and Spanish only ($y$) is 0. - The intersection of all three languages is 1. - The number of students studying French only is 7. - The number of students studying Arabic total is 8. 4. **Calculate $x$ (Arabic and French only):** Arabic total = A only + Arabic and French only + Arabic and Spanish only + all three $$8 = 2 + x + 0 + 1$$ $$8 = 3 + x$$ $$x = 8 - 3 = 5$$ 5. **Check total students:** Sum all regions: - French only: 7 - Spanish only: 5 - Arabic only: 2 - French and Spanish only: 4 - Arabic and French only: 5 - Arabic and Spanish only: 0 - All three: 1 Total: $$7 + 5 + 2 + 4 + 5 + 0 + 1 = 24$$ Since total students are 25, the remaining 1 student must be outside all three languages (studying none). 6. **Final Venn diagram numbers:** - F only: 7 - S only: 5 - A only: 2 - F and S only: 4 - A and F only: 5 - A and S only: 0 - All three: 1 - None: 1 **Answer:** The missing numbers are $5$ for Arabic and French only, $0$ for Arabic and Spanish only, and $7$ for French only as given.