Find the value of two numbers if their sum is 11 and their difference is 3
2 answers:
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Answer:
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′