A faculty consists of a group of teachers and cannot exist without them. The faculty may work in buildings (choice a), but the buildings aren't essential. They may use textbooks (choice b) and attend meetings (choice d), but these aren't essential either.
A cage is meant to keep something surrounded, so enclosure is the essential element. A prisoner (choice b) or an animal (choice c) are two things that may be kept in cages, among many other things. A zoo (choice d) is only one place that has cages.
A directory is a listing of names or things, so choice b is the essential element. A telephone (choice a) often has a directory associated with it, but it is not essential. A computer (choice c) uses a directory format to list files, but it is not required. Names (choice d) are often listed in a directory, but many other things are listed in directories, so this is not the essential element.
An agreement is necessary to have a contract. A contract may appear on a document (choice b), but it is not required. A contract may be oral as well as written, so choice c is not essential. A contract can be made without an attorney (choice d).
A saddle is something one uses to sit on an animal, so it must have a seat (choice b). A saddle is often used on a horse (choice a), but it may be used on other animals. Stirrups (choice c) are often found on a saddle but may not be used. A horn (choice d) is found on Western saddles, but not English saddles, so it is not the essential element here.
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