A is the set of all even natural numbers, and B is the set of all odd natural numbers. Describe a universal set for A and B. Also, with respect to this universal set, give a relationship between A and B.
To describe a universal set for A and B, we need to consider a set that contains all the elements from both A and B.
In this case, we can define the universal set as the set of all natural numbers including both even and odd numbers. We can represent this universal set as U = {1, 2, 3, 4, 5, 6, ...}.
With respect to this universal set, we can describe the relationship between sets A and B. Since A is the set of even natural numbers, we can write A = {2, 4, 6, 8, ...}. On the other hand, B is the set of odd natural numbers, so B = {1, 3, 5, 7, ...}.
The relationship between A and B is that they are mutually exclusive subsets of the universal set. In other words, there are no common elements shared between A and B.
The universal set for A and B, in this case, would be the set of all natural numbers.
With respect to this universal set, the relationship between A and B is that they are disjoint sets, meaning they have no elements in common. Every natural number is either even (in set A) or odd (in set B), but not both.