Question

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={ , , }}

Answer 1

a)
`A' = [0,2,6,8]`

b)
`(AUB)' = [0,2,6]`

c)
`(AUB')' = [9]`

d) A∩B′
`= [3,5,9]`

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]`

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]`

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]`

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]`

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

`AUB' = [0,1,2,3,4,5,6,7,9]`

And then the complment is just:

`(AUB')' = [9]`

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]`