Question
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
Let sets
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
-
Find
: - Set
- Set
- Set
First, find: Then, find the intersection with: So, - Set
-
Find
:
List all distinct elements from the three sets:- From
: - From
: - From
:
Combining, we have: - From
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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.
1, 2, 4, 5, 6, 7, 8, 10.
Thus, we have:
.
Finally, we write the results: