Let U = {0, 1, 2, 3, 4, 5,...}, A = {1, 2, 3, 4,...}, B = {4, 8, 12, 16,...}, and C = {2, 4, 6, 8,...}. Determine the following:

A′ ∩ C

Are you looking for the intersection of sets A and C?

If A is all real numbers >/= 1
and C is all real EVEN numbers >/= 2

Then everything in C is in A and C is a sub set of A and C is itself the intersection of the two sets.

so confusing :(

Use Venn diagrams.

http://mathworld.wolfram.com/VennDiagram.html

To find A' ∩ C, we first need to find A' (the complement of A) and then find the intersection of A' and C.

1. Finding A':
The complement of A, denoted as A', is the set of all elements in the universal set U that are not in A.
Since A = {1, 2, 3, 4, ...} and U = {0, 1, 2, 3, 4, 5, ...}, to find A', we need to remove all the elements in A from U. This means we need to remove 1, 2, 3, 4, ... from the set U.

Removing these elements, we get A' = {0, 5, 6, 7, 8, 9, 10, 11, ...}.

2. Finding A' ∩ C:
The intersection of two sets A' and C is the set of elements that are common to both sets.

A' = {0, 5, 6, 7, 8, 9, 10, 11, ...}
C = {2, 4, 6, 8, ...}

Looking at the sets, we can see that the only common element is 6. Therefore, A' ∩ C = {6}.

So, A' ∩ C = {6}.