Final answer:
To determine the permission setting for a new schema directory in a database system, one would typically use the command GRANT. However, for file system permissions on a Unix/Linux system, umask would be used, and for permissions in Hadoop, the HDFS permission system would apply. Kerberos is used for network authentication and not directly for setting permissions.
Step-by-step explanation:
When you need to determine the permission setting for a new schema directory, the appropriate tool to use depends on the context of the system and environment you are working with. If we are dealing with a relational database management system (RDBMS), the correct tool would be B. GRANT. This command is used to set permissions in SQL databases, allowing users to access specific database objects based on their privileges. However, if we are dealing with permissions in a Linux/Unix file system, umask would be the command to set default permissions for newly created files and directories. In the context of management of the Hadoop File System, HDFS permissions are managed internally using Hadoop's own permission mechanism. Lastly, Kerberos is an authentication protocol used to verify the identities of users or nodes in a network; it does not directly manage file or directory permissions.