Final answer:
The solution set of 0 is empty with the empty set ∅, possibly contains 0 with the set of natural numbers N (depending on definition), includes 0 with the set of integers Z, and contains 0 with the set of real numbers R.
Step-by-step explanation:
The question asks to describe and compare the solution sets of 0 with different sets: the empty set (∅), the set of natural numbers (N), the set of integers (Z), and the set of real numbers (R). To clarify, the solution set of 0 would be a set that contains the number 0 if such a number is included in the set being compared.
- Solution Set of 0 with ∅: The empty set has no elements, so the solution set of 0 with the empty set is also an empty set because 0 is not an element of ∅.
- Solution Set of 0 with N: The set of natural numbers traditionally includes positive integers starting from 1. However, in some definitions, the set of natural numbers includes 0. If we use this definition, the solution set of 0 with N would include the number 0. If we do not include 0 in N, then the solution set would be empty, similar to the empty set.
- Solution Set of 0 with Z: The set of integers includes all whole numbers, both positive and negative, including 0. Hence, the solution set of 0 with Z includes the number 0.
- Solution Set of 0 with R: The set of real numbers includes all rational and irrational numbers, which means it also includes whole numbers such as 0. Thus, the solution set of 0 with R includes the number 0.
In summary, the solution sets containing 0 will be empty with the empty set (∅), possibly empty or containing 0 with N (depending on the definition of natural numbers being used), and will definitely contain 0 with both Z and R.