Answers
A' = {1,4,5,6}
B' = {1,2,6}
A′ ∩ B′ = {1, 6}
A ∪ B = {2,3,4,5}
The venn diagram is shown below.
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Step-by-step explanation
Start with set U = {1,2,3,4,5,6}. This is the universal set.
Erase items "2" and "3" which are found in set A. This forms set A prime or A', which is the complement of set A. It's the complete opposite of set A. If something is in A, then it is not in set A', and vice versa.
A' = {1,4,5,6}
The same idea applies with B'. We start with U = {1,2,3,4,5,6} and erase "3", "4" and "5" to get
B' = {1,2,6}
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We found that
A' = {1,4,5,6}
B' = {1,2,6}
The only things in common to both sets are the "1" and "6". These values are found in the intersection of the two sets.
Therefore,
A′ ∩ B′ = {1, 6}
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The set union of A and B is:
A U B = {2,3,4,5}
These values are found in set A, set B or both sets at the same time.
The opposite or complement of this would be
( A ∪ B )′ = {1, 6}
Which is exactly what we got with A′ ∩ B′
This example helps show ( A ∪ B )′ = A′ ∩ B′.