In this context, the universal set would be all integers. The universal set is the set that contains all possible elements being considered in a particular discussion. Since Carrie is looking for even numbers within the set of prime numbers, it is logical to start from the broader category of integers that encompasses both even and prime numbers.
Here’s how the options break down:
- All real numbers: This set includes all rational and irrational numbers, not just integers, so it's broader than needed.
- All integers: This set contains all whole numbers, both positive and negative, which is relevant for the discussion of even and prime numbers.
- Prime numbers: This only includes prime numbers and does not encompass every even number, so it's not the universal set for this context.
- Even numbers: This set contains only even numbers and does not include prime numbers, leading us to a narrow scope.
Thus, the best choice for the universal set in this scenario is all integers.
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