Final answer:
The task of establishing the physical database and its logical relations within a corporate information services department is the responsibility of the Database Administration function.
Step-by-step explanation:
Within a corporate information services department, the task of establishing the physical database and its logical relations are responsibilities of the Database Administration function. The Database Administrator (DBA) is in charge of the design, implementation, maintenance, and repair of an organization's database. They are responsible for developing and managing the database structure, ensuring the integrity of the data, maintaining database performance, and implementing security measures to safeguard the data. The role of the DBA is crucial, as it ensure that data is available to users and secure from unauthorized access. Therefore, the correct answer is b. Database Administration.