Final answer:
The extension is the set of n-tuples of members of the domain of discourse assigned to a given n-place predicate letter.
Step-by-step explanation:
The set of n-tuples of members of the domain of discourse assigned to a given n-place predicate letter (for any n greater than zero) in an interpretation is called the extension.
For example, let's say we have a predicate letter P with a domain of discourse {1, 2, 3}. The extension of P would be the set of all possible n-tuples (or combinations) of members of the domain, such as {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}.
Understanding the concept of extensions is important in logic and mathematics because it allows us to precisely define the meaning of predicate letters and evaluate their truth values in different interpretations.