Distinguish Checked and Unchecked Exceptions in Java

What is the difference between checked and unchecked exceptions in Java? Give examples and explain what the distinction requires at a method boundary. ### What a Strong Answer Covers Identify the relevant exception hierarchy, explain catch-or-declare checking, and distinguish compile-time obligations from the time an exception is actually thrown. Discuss recovery and propagation without treating every unchecked exception as safe to ignore. ### Follow-up Questions - Does declaring throws handle an exception? - What should a library preserve when translating one exception into another?