Step 1: List all entities with their original attributes and primary keys
E₁: Attributes A, B, C, primary key M
E₂: Attributes D, E, primary key N
E₃: Attributes F, G, primary key F
E₄: Attributes K, L, primary key K
E₅: Attributes H, I, J, primary key H
Step 2: Identify foreign keys from relationships
R₁: E₁—E₂ → include primary key M (E₁) in E₂ as foreign key
R₂: E₂—E₃ → include primary key N (E₂) in E₃
R₃: E₂—E₃ → include primary key N (E₂) in E₃ (already accounted for)
R₄: E₁—E₄ → include primary key M (E₁) in E₄
R₅: E₃—E₅ → include primary key F (E₃) in E₅
R₆: E₃—E₅ → include primary key F (E₃) in E₅ (already accounted for)
Step 3: Count attributes per relation after minimization
E₁: A, B, C, M → 4 attributes
E₂: D, E, N (primary key) → 3 attributes
E₃: F, G, N (from E₂), F (primary key) → 3 attributes
E₄: K, L, M (from E₁) → 3 attributes
E₅: H, I, J, F (from E₃) → 4 attributes
Step 4: Sum total attributes
4 (E₁) + 3 (E₂) + 3 (E₃) + 3 (E₄) + 4 (E₅) = 17
Step 5: Conclusion
Total attributes = 17, which is not 18.
correct answer is None of the these
