Let u= u= universal set ={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}={0, 1, 2, 3, 4, 5, 6, 7, 8, 9} , a={1, 3, 4, 5, 7, 9} a={1, 3, 4, 5, 7, 9} , and b={1, 4, 7, 8} b={1, 4, 7, 8}. list the elemetns of the following sets in the increasing order: aâ²={aâ²={ , , , }} (aâªb)â²={(aâªb)â²={ , , }} (aâªbâ²)â²={(aâªbâ²)â²={ }} aâ©bâ²={aâ©bâ²={ , , }}

a)

b)

c)

d) A∩B′

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:

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:

And now the complement for (AUB)' are the elements that are not in AUB but are on the universal set and we got:

Part c

For this case we need to find B' who are the elements on the universal set that are not in B

Then we can find the union between AUB' and we got:

And then the complment is just:

Part d

For this case we just need to see the elements in common between A and B' and we got:

A∩B′