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
A' is the set of all elements of U which are not in A
= {0}
so A' ∩ C = {0} ∩ {2,4,6,8,..} = Ø or {} or null set
Thank you Reiny. I actually got the same answer you did. Guess I understand it better than I thought. I just wanted to be sure I was doing it right. Thanks again :)
To determine the intersection of sets A' and C, we first need to find the complement of A.
The complement of set A, denoted as A', is the set of all elements in the universal set U that are not in A.
Given that A = {1, 2, 3, 4, ...}, we can see that the complement of A would be all the numbers in set U that are not in set A. So, A' would include all elements in U except for 1, 2, 3, 4, and so on.
Since U = {0, 1, 2, 3, 4, 5, ...}, A' would be {0, 5, 6, 7, 8, ...}.
Now, to find the intersection of A' and C, we need to identify the elements that are common to both sets A' and C.
C = {2, 4, 6, 8, ...}, and A' = {0, 5, 6, 7, 8, ...}.
From these sets, we can see that the only element they have in common is 6.
Thus, the intersection of A' and C, denoted as A' ∩ C, is the set {6}.