Final answer:
The sets that have the set of rational numbers Q as a proper subset are the set of positive integer numbers, the set of integers, and the set of natural numbers.
Step-by-step explanation:
To determine which sets have the set of rational numbers Q as a proper subset, we need to understand what a proper subset is. A proper subset is a subset that contains some but not all of the elements of a set. In other words, it is a subset that is not equal to the original set.
The set of rational numbers Q includes fractions and integers, so any set that contains only integers or positive integers (options C and D) would be a proper subset of Q. Additionally, the set of natural numbers N, which includes positive integers, would also be a proper subset of Q.
Therefore, options C, D, and G have the set of rational numbers Q as a proper subset.