Final answer:
The domain in mathematics is the set of all possible inputs for a given relation or function, represented by the x-values in ordered pairs or the set of all possible values for a variable in a given context.
Step-by-step explanation:
The domain of a relation in mathematics refers to the set of all possible inputs or x-values for which the relation is defined. When given a set of ordered pairs, the domain consists of all the first elements in each pair. When considering the experiment with drawing cards until the Queen of Hearts is drawn, the domain represents the possible number of draws it could take right from 1 draw to theoretically infinity (in practice, it would be a large number depending on when the Queen of Hearts is actually drawn).
However, if we consider 'X' as a student's major, the domain of 'X' would be the set of all possible majors that students could declare. Similarly, for 'Y' being the number of classes taken in the previous semester, the domain would be the set of all non-negative integers that represent the number of classes a student could have taken. Lastly, 'Z' represents the amount of money spent on books in the previous semester, so the domain would again be all non-negative real numbers (assuming one can't spend a negative amount).