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.
Now, what happens when I take all the even natural numbers, such as 2,4,6,8,...
and combine them with the set of all odd natural numbers, which would be 1,3,5,7,... ?
I don't know they would make up all the numbers
To describe a universal set for the sets A and B, we need to identify a set that contains all the elements that belong to A and B. In this case, the universal set can be the set of all natural numbers.
The set of all natural numbers can be denoted as N = {1, 2, 3, 4, 5, ...}. It contains every possible natural number, including both even and odd numbers.
With respect to this universal set, we can see that A (the set of all even natural numbers) contains elements that are divisible by 2, while B (the set of all odd natural numbers) contains elements that are not divisible by 2. Therefore, A and B are disjoint sets since they do not share any common elements.
In terms of relationship, A and B can be considered as complementary sets within the universal set N. This means that every element in the universal set N belongs either to A or B, but never to both.