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

To determine A′ ∩ C, we need to find the intersection of the complement of set A and set C.

First, let's find the complement of A, denoted as A′. The complement of A is the set of all elements in the universal set U that are not in A.

Since A = {1, 2, 3, 4,...}, A′ would include all the elements in U except for 1, 2, 3, 4, and so on.

The universal set U is defined as U = {0, 1, 2, 3, 4, 5,...}. Therefore, A′ = {0, 5, 6, 7, 8, 9,...}.

Next, we find the intersection of A′ and C. The intersection of two sets A and B is the set of elements that are common to both A and B.

C = {2, 4, 6, 8,...} and A′ = {0, 5, 6, 7, 8, 9,...}, so the intersection of A′ and C is {6, 8,...}.

Therefore, A′ ∩ C = {6, 8,...}.