Answered

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]\[ A=\{1,8,9,11,12,13,15,17,18\} \][/tex]
[tex]\[ B=\{1,2,7,8,9,20\} \][/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.



Answer :

GinnyAnswer
Let's start by defining what we need to find:

### Step 1: Find [tex]\( A \cup B \)[/tex]
The union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] (denoted [tex]\( A \cup B \)[/tex]) consists of all elements that are in [tex]\( A \)[/tex], [tex]\( B \)[/tex], or both. To find this, we list all unique elements from both sets:

- Elements in [tex]\( A \)[/tex]: [tex]\( \{1, 8, 9, 11, 12, 13, 15, 17, 18\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 7, 8, 9, 20\} \)[/tex]

Combining these sets and removing duplicates, we obtain:
[tex]\[ A \cup B = \{1, 2, 7, 8, 9, 11, 12, 13, 15, 17, 18, 20\} \][/tex]

### Step 2: Find [tex]\( A \cap B \)[/tex]
The intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] (denoted [tex]\( A \cap B \)[/tex]) consists of all elements that are common to both sets. To find this, we list the elements present in both [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:

- Common elements: [tex]\( \{1, 8, 9\} \)[/tex]

Thus, we have:
[tex]\[ A \cap B = \{1, 8, 9\} \][/tex]

### Final Solution
- [tex]\( A \cup B = \{1, 2, 7, 8, 9, 11, 12, 13, 15, 17, 18, 20\} \)[/tex]
- [tex]\( A \cap B = \{1, 8, 9\} \)[/tex]

So, the complete answer is:
[tex]\[ A \cup B = \{1, 2, 7, 8, 9, 11, 12, 13, 15, 17, 18, 20\} \][/tex]
[tex]\[ A \cap B = \{1, 8, 9\} \][/tex]