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Let [tex]\( U \)[/tex] be the universal set, where:
[tex]\[ U = \{1, 2, 3, \ldots, 18, 19, 20\} \][/tex]

Let sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] be subsets of [tex]\( U \)[/tex], where:
[tex]\[ A = \{2, 4, 5, 10, 13, 17, 19\} \][/tex]
[tex]\[ B = \{1, 4, 6, 8, 9, 10, 13, 14, 15, 16, 17\} \][/tex]

Find the following:

1. List the elements in the set [tex]\( A \cup B \)[/tex]:
[tex]\[ A \cup B = \{ \}
\square \][/tex]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.

2. List the elements in the set [tex]\( A \cap B \)[/tex]:
[tex]\[ A \cap B = \{ \}
\square \][/tex]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.

You may want to draw a Venn Diagram to help answer this question.

Sagot :

GinnyAnswer
To find the sets [tex]\( A \cup B \)[/tex] and [tex]\( A \cap B \)[/tex], we need to understand the operations of union and intersection between the sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex].

### Step-by-Step Solution

1. Understanding Union ([tex]\( A \cup B \)[/tex]):
The union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of all elements that are in [tex]\( A \)[/tex], in [tex]\( B \)[/tex], or in both sets. In other words, [tex]\( A \cup B \)[/tex] includes every unique element from both sets.

2. Understanding Intersection ([tex]\( A \cap B \)[/tex]):
The intersection of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of all elements that are both in [tex]\( A \)[/tex] and [tex]\( B \)[/tex].

### Given Sets:
- [tex]\( A = \{2, 4, 5, 10, 13, 17, 19\} \)[/tex]
- [tex]\( B = \{1, 4, 6, 8, 9, 10, 13, 14, 15, 16, 17\} \)[/tex]

3. Finding [tex]\( A \cup B \)[/tex] (Union):
We list all unique elements that are either in [tex]\( A \)[/tex], [tex]\( B \)[/tex], or both.
[tex]\[ A \cup B = \{1, 2, 4, 5, 6, 8, 9, 10, 13, 14, 15, 16, 17, 19\} \][/tex]

4. Finding [tex]\( A \cap B \)[/tex] (Intersection):
We list the elements that are common in both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
[tex]\[ A \cap B = \{4, 10, 13, 17\} \][/tex]

### Final Answer

- Elements in the set [tex]\( A \cup B \)[/tex]:
[tex]\[ A \cup B = \{1, 2, 4, 5, 6, 8, 9, 10, 13, 14, 15, 16, 17, 19\} \][/tex]

- Elements in the set [tex]\( A \cap B \)[/tex]:
[tex]\[ A \cap B = \{4, 10, 13, 17\} \][/tex]
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