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
Hehehehe! I'm sorry, but my math skills don't go beyond about 7th grade.
lol ok thanx n e way
To determine A' ∩ C, we first need to find the complement of set A and then find the intersection of that complement with set C.
The complement of set A (A') contains all the elements in the universal set U that are not in set A. In this case, A = {1, 2, 3, 4,...}, and U = {0, 1, 2, 3, 4, 5,...}. Therefore, the complement of set A is the set of all non-negative integers that are not in A.
Complement of A (A') = {0, 5, 6, 7, 8, 9, 10, 11, 12, 13,...}
Now, to find A' ∩ C, we need to find the intersection of the complement of A (A') with set C.
A' ∩ C = {0, 5, 6, 7, 8, 9, 10, 11, 12, 13,...} ∩ {2, 4, 6, 8,...}
The intersection of two sets contains all the elements that are common to both sets. In this case, the elements that are present in both sets A' and C are the even numbers.
Therefore, A' ∩ C = {2, 4, 6, 8,...}
So, A' ∩ C is the set of even numbers.