Final answer:
The domain and range of a relation define all possible inputs and outputs respectively, which can be numerical sets or descriptive categories. These concepts ensure the reliability of mathematical calculations and data analysis. a) Domain: All real numbers; Range: All real numbers
Step-by-step explanation:
The question asks us to identify the domain and range of various relations, which are fundamental concepts in mathematics, specifically in the study of functions. The domain of a relation or function is the set of all possible inputs, while the range is the set of all possible outputs.
For instance, if X represents a student's major, the domain would include all majors offered by the university. If Y represents the number of classes taken in the previous semester, the domain would consist of all non-negative integers up to the maximum number of classes allowed.
The domain of Z, representing the amount of money spent on books, would be all non-negative real numbers, as one cannot spend a negative amount of money on books. Therefore, potential domains and ranges can be either numerical values or descriptive categories, and they serve as 'guard rails' to ensure the validity and reliability of mathematical calculations or data collection.