Given that u = {1,2,3,4,5,6,7,8,9}, A ={2,3,4,5} and B= {4,5,7,8}, list the following sets:
i) Au (A1nB)
ii) Bu (A1n B)
iii) Au (AnB1)
iv) B1u (AnB1)
v) A u(A1nB1)
usually if you don't get an answer to your question the reason might be that your notation is not understood, or the question is too ambiguous.
I am trying to guess that than you are using "u" to stand for union and "n" to stand for intersection?
But what is A1 ? Is it supposed to say A' or not(A) ?
Yes "U" stand for union "n" stand for intersection. The A1 is supposed to A'.
To solve these set operation questions, we need to understand the concepts of union (u) and intersection (n).
1. A u (A n B):
To find this set, we first need to determine the intersection of sets A and B, which contains the common elements.
A n B = {4, 5}
Now, we can find the union of set A and the intersection of A and B.
A u (A n B) = {2, 3, 4, 5}
2. B u (A n B):
Similarly, we will find the intersection of sets A and B, which is {4, 5}.
B u (A n B) = {4, 5, 7, 8}
3. A u (AnB1):
Here, AnB1 means the intersection of set A and the complement of set B.
To find the complement of set B, we need to find the elements in the universal set u that are not in set B.
B's complement = u - B = {1, 2, 3, 6, 9}
Now, we find the intersection of set A and the complement of set B.
A n B1 = {2, 3}
A u (AnB1) = {2, 3, 4, 5, 6, 7, 8, 9}
4. B1 u (AnB1):
B1 means the complement of set B.
B1 = u - B = {1, 2, 3, 6, 9}
Now, we find the intersection of set A and the intersection of A and the complement of set B.
AnB1 = {2, 3}
B1 u (AnB1) = {1, 2, 3, 6, 9, 2, 3} (Note: Since sets only contain unique elements, duplicate numbers are ignored)
5. A u (A1 n B1):
Here, A1 represents the complement of set A and B1 represents the complement of set B.
A1 = u - A = {1, 6, 7, 8, 9}
B1 = u - B = {1, 2, 3, 6, 9}
Now, we find the intersection of A1 and B1.
A1 n B1 = {1, 6, 9}
Finally, we find the union of set A and the intersection of A1 and B1.
A u (A1 n B1) = {1, 2, 3, 4, 5, 6, 7, 8, 9}
So, the list of the sets are:
i) A u (A n B) = {2, 3, 4, 5}
ii) B u (A n B) = {4, 5, 7, 8}
iii) A u (A n B1) = {2, 3, 4, 5, 6, 7, 8, 9}
iv) B1 u (A n B1) = {1, 2, 3, 6, 9}
v) A u (A1 n B1) = {1, 2, 3, 4, 5, 6, 7, 8, 9}