Assess students' ability to design an efficient relational schema for a library management system by applying normalization up to Third Normal Form (identify functional dependencies, eliminate redundancy, decompose relations with lossless join and dependency preservation), specify primary and foreign keys, and recommend indexing strategies (index types, composite/covering indexes, clustered vs nonclustered) to optimize common queries such as book lookup, circulation records, and overdue checks. Ask for SQL DDL for the normalized schema, sample queries demonstrating index use, and a brief justification of any recommended denormalization or index trade-offs for performance.