Sure! Let's solve this step by step.
### Step 1: Finding [tex]\( A \cup B \)[/tex]
The union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], denoted as [tex]\( A \cup B \)[/tex], is the set of all distinct elements that are in either [tex]\( A \)[/tex] or [tex]\( B \)[/tex] or in both.
Given:
[tex]\[ A = \{5, 6, 7, 8, 9, 10\} \][/tex]
[tex]\[ B = \{2, 3, 4, 5, 11, 12, 13\} \][/tex]
To find [tex]\( A \cup B \)[/tex], we combine all unique elements from both sets:
[tex]\[ A \cup B = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\} \][/tex]
### Step 2: Finding [tex]\( A \cap B \)[/tex]
The intersection of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], denoted as [tex]\( A \cap B \)[/tex], is the set of all elements that are common to both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
Given:
[tex]\[ A = \{5, 6, 7, 8, 9, 10\} \][/tex]
[tex]\[ B = \{2, 3, 4, 5, 11, 12, 13\} \][/tex]
To find [tex]\( A \cap B \)[/tex], we extract the elements that exist in both sets:
[tex]\[ A \cap B = \{5\} \][/tex]
### Answers:
1. [tex]\( A \cup B = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\} \)[/tex]
2. [tex]\( A \cap B = \{5\} \)[/tex]
These are the required results.
