Answer:
a) ![A' = [0,2,6,8]](https://tex.z-dn.net/?f=%20A%27%20%3D%20%5B0%2C2%2C6%2C8%5D)
b) ![(AUB)' = [0,2,6]](https://tex.z-dn.net/?f=%20%28AUB%29%27%20%3D%20%5B0%2C2%2C6%5D)
c) ![(AUB')' = [9]](https://tex.z-dn.net/?f=%20%28AUB%27%29%27%20%3D%20%5B9%5D)
d) A∩B′![= [3,5,9]](https://tex.z-dn.net/?f=%3D%20%5B3%2C5%2C9%5D)
Step-by-step explanation:
Assuming this problem: "Let U= U= Universal set ={0, 1, 2, 3, 4, 5, 6, 7, 8, 9} , A={1, 3, 4, 5, 7, 9} , and B={1, 4, 7, 8} . List the elemetns of the following sets in the increasing order: a) A′= b) (A∪B)′={ , , }} c) (A∪B′)′={ }} d) A∩B′={ , , }}"
Part a
For this case we just need to find the elements in the universal set that are not in A. And we see that:
![A' = [0,2,6,8]](https://tex.z-dn.net/?f=%20A%27%20%3D%20%5B0%2C2%2C6%2C8%5D)
And that represent the complement for A
Part b
For this case we need to find first the Union AUB who are the elements on A or B without repetition and we got:
![AUB = [1,3,4,5,7,8,9]](https://tex.z-dn.net/?f=%20AUB%20%3D%20%5B1%2C3%2C4%2C5%2C7%2C8%2C9%5D)
And now the complement for (AUB)' are the elements that are not in AUB but are on the universal set and we got:
![(AUB)' = [0,2,6]](https://tex.z-dn.net/?f=%20%28AUB%29%27%20%3D%20%5B0%2C2%2C6%5D)
Part c
For this case we need to find B' who are the elements on the universal set that are not in B
![B' = [0,2,3,5,6,9]](https://tex.z-dn.net/?f=%20B%27%20%3D%20%5B0%2C2%2C3%2C5%2C6%2C9%5D)
Then we can find the union between AUB' and we got:
![AUB' = [0,1,2,3,4,5,6,7,9]](https://tex.z-dn.net/?f=%20AUB%27%20%3D%20%5B0%2C1%2C2%2C3%2C4%2C5%2C6%2C7%2C9%5D)
And then the complment is just:
![(AUB')' = [9]](https://tex.z-dn.net/?f=%20%28AUB%27%29%27%20%3D%20%5B9%5D)
Part d
For this case we just need to see the elements in common between A and B' and we got:
A∩B′![= [3,5,9]](https://tex.z-dn.net/?f=%3D%20%5B3%2C5%2C9%5D)