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Let be the universal set.
Let sets , and be subsets of , where:
Set
Set
Set
LIST the elements in the set :

LIST the elements in the set

Ask by Crawford Washington. in the United States
Mar 22,2025

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Solution

  1. Find :
    • Set
    • Set
    • Set
    First, find :
    Then, find the intersection with :
    So,
  2. Find :
    List all distinct elements from the three sets:
    • From :
    • From :
    • From :
    Combining, we have:

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Simplify this solution

Beyond the Answer

Let’s start with , the intersection of the sets. To find this, we look for elements that are present in all three sets , , and .
  • Set
  • Set
  • Set
Checking each element in set :
  • 4 is in , but not in .
  • 6 is in , but not in .
  • 10 is in , but not in .
Thus, there are no common elements in all three sets:
.
Now, let’s compute , the union of the sets. To find this, we combine all the unique elements from each set.
Identifying the unique elements:
  • From : 4, 6, 10
  • From : 2, 4, 6, 7 (2 and 7 are new)
  • From : 1, 2, 5, 8, 10 (1, 5, and 8 are new)
Combining these, the unique elements are:
1, 2, 4, 5, 6, 7, 8, 10.
Thus, we have:
.
Finally, we write the results:

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