Keys and Candidate-Key Constraints for $(StudentName,\ StudentAge)$: Solving the “$X$ cannot be …” Problem

The content explains how standard ER‑to‑relational mapping rules validate three statements about weak entities, partial keys, and many‑to‑many relationships, and shows that the fourth claim—every generated relation has only one candidate key—is false.

• Weak entities depend on a strong owner and are identified by the owner’s primary key plus a partial (discriminator) key.
• A partial key is allowed for weak entities, forming a composite primary key with the owner key.
• Binary $M:N$ relationships are mapped to a separate associative relation containing the participating primary keys.
• A generated relation may have multiple candidate keys; one is chosen as the primary key, so statement (iv) is false.

The Banker's Algorithm is a deadlock‑avoidance method that keeps a system in a safe state by checking each resource request against the maximum declared needs of processes.

• Maintains Available, Max, Allocation, and Need matrices, where $\text{Need}[i][j]=\text{Max}[i][j]-\text{Allocation}[i][j]$.
• The Safety Algorithm uses vectors Work and Finish to find an execution order; if all processes finish, the state is safe.
• The Resource‑Request Algorithm simulates allocation, runs the safety check, and commits only if the resulting state remains safe.
• Time complexity of the safety check is $O(m \times n^{2})$.
• In practice the algorithm is rarely used because processes must predeclare maximum needs and the algorithm’s overhead is high.