Final answer:
The Java Servlet Container is responsible for hosting the execution of a Web service in a Java SOC development environment.
Step-by-step explanation:
The component in a Java SOC development environment that is responsible for hosting the execution of a Web service is the Java Servlet Container. The Java Servlet Container is a runtime environment that provides the necessary infrastructure to host and execute Java servlets, which are used to implement web services in Java. It manages the lifecycle of the servlets, handles HTTP requests and responses, and provides the necessary network communication layer.