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Sagot :
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]
### 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]
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