Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To solve this question, let's evaluate the set operations one by one. We'll match the correct sets to each operation based on the provided sets [tex]\( A, B, \)[/tex] and [tex]\( C \)[/tex].
Given:
- [tex]\( A = \{1, 2, 3, 4, 5\} \)[/tex]
- [tex]\( B = \{2, 4, 6\} \)[/tex]
- [tex]\( C = \{1, 3, 5\} \)[/tex]
Let's consider each operation step by step:
1. [tex]\( B \cap C \)[/tex]: This is the intersection of sets [tex]\( B \)[/tex] and [tex]\( C \)[/tex], which includes elements common to both sets.
- [tex]\( B \cap C = \{2, 4, 6\} \cap \{1, 3, 5\} = \emptyset \)[/tex]
(since there are no common elements).
So, [tex]\( B \cap C \)[/tex] matches the empty set (null set).
2. [tex]\( A \cap C \)[/tex]: This is the intersection of sets [tex]\( A \)[/tex] and [tex]\( C \)[/tex], which includes elements common to both sets.
- [tex]\( A \cap C = \{1, 2, 3, 4, 5\} \cap \{1, 3, 5\} = \{1, 3, 5\} \)[/tex].
So, [tex]\( A \cap C \)[/tex] matches [tex]\(\{1, 3, 5\}\)[/tex].
3. [tex]\( A \cup C \)[/tex]: This is the union of sets [tex]\( A \)[/tex] and [tex]\( C \)[/tex], which includes all elements from both sets without repetition.
- [tex]\( A \cup C = \{1, 2, 3, 4, 5\} \cup \{1, 3, 5\} = \{1, 2, 3, 4, 5\} \)[/tex].
So, [tex]\( A \cup C \)[/tex] matches [tex]\( \{1, 2, 3, 4, 5\} \)[/tex].
4. [tex]\( A \cap B \)[/tex]: This is the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], which includes elements common to both sets.
- [tex]\( A \cap B = \{1, 2, 3, 4, 5\} \cap \{2, 4, 6\} = \{2, 4\} \)[/tex].
So, [tex]\( A \cap B \)[/tex] matches [tex]\(\{2, 4\}\)[/tex].
5. [tex]\( A \cup B \)[/tex]: This is the union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], which includes all elements from both sets without repetition.
- [tex]\( A \cup B = \{1, 2, 3, 4, 5\} \cup \{2, 4, 6\} = \{1, 2, 3, 4, 5, 6\} \)[/tex].
So, [tex]\( A \cup B \)[/tex] matches [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex].
Final matching:
1. [tex]\( B \cap C \)[/tex] [tex]$\square$[/tex] [tex]\(\emptyset\)[/tex]
2. [tex]\( A \cap C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 3, 5\}\)[/tex]
3. [tex]\( A \cup C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5\}\)[/tex]
4. [tex]\( A \cap B \)[/tex] [tex]$\square$[/tex] [tex]\(\{2, 4\}\)[/tex]
5. [tex]\( A \cup B \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex]
Now, you can fill in the blanks based on this matching:
1. [tex]\( B \cap C \)[/tex] [tex]$\square$[/tex] null (empty set)
2. [tex]\( A \cap C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 3, 5\}\)[/tex]
3. [tex]\( A \cup C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5\}\)[/tex]
4. [tex]\( A \cap B \)[/tex] [tex]$\square$[/tex] [tex]\(\{2, 4\}\)[/tex]
5. [tex]\( A \cup B \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex]
Given:
- [tex]\( A = \{1, 2, 3, 4, 5\} \)[/tex]
- [tex]\( B = \{2, 4, 6\} \)[/tex]
- [tex]\( C = \{1, 3, 5\} \)[/tex]
Let's consider each operation step by step:
1. [tex]\( B \cap C \)[/tex]: This is the intersection of sets [tex]\( B \)[/tex] and [tex]\( C \)[/tex], which includes elements common to both sets.
- [tex]\( B \cap C = \{2, 4, 6\} \cap \{1, 3, 5\} = \emptyset \)[/tex]
(since there are no common elements).
So, [tex]\( B \cap C \)[/tex] matches the empty set (null set).
2. [tex]\( A \cap C \)[/tex]: This is the intersection of sets [tex]\( A \)[/tex] and [tex]\( C \)[/tex], which includes elements common to both sets.
- [tex]\( A \cap C = \{1, 2, 3, 4, 5\} \cap \{1, 3, 5\} = \{1, 3, 5\} \)[/tex].
So, [tex]\( A \cap C \)[/tex] matches [tex]\(\{1, 3, 5\}\)[/tex].
3. [tex]\( A \cup C \)[/tex]: This is the union of sets [tex]\( A \)[/tex] and [tex]\( C \)[/tex], which includes all elements from both sets without repetition.
- [tex]\( A \cup C = \{1, 2, 3, 4, 5\} \cup \{1, 3, 5\} = \{1, 2, 3, 4, 5\} \)[/tex].
So, [tex]\( A \cup C \)[/tex] matches [tex]\( \{1, 2, 3, 4, 5\} \)[/tex].
4. [tex]\( A \cap B \)[/tex]: This is the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], which includes elements common to both sets.
- [tex]\( A \cap B = \{1, 2, 3, 4, 5\} \cap \{2, 4, 6\} = \{2, 4\} \)[/tex].
So, [tex]\( A \cap B \)[/tex] matches [tex]\(\{2, 4\}\)[/tex].
5. [tex]\( A \cup B \)[/tex]: This is the union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], which includes all elements from both sets without repetition.
- [tex]\( A \cup B = \{1, 2, 3, 4, 5\} \cup \{2, 4, 6\} = \{1, 2, 3, 4, 5, 6\} \)[/tex].
So, [tex]\( A \cup B \)[/tex] matches [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex].
Final matching:
1. [tex]\( B \cap C \)[/tex] [tex]$\square$[/tex] [tex]\(\emptyset\)[/tex]
2. [tex]\( A \cap C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 3, 5\}\)[/tex]
3. [tex]\( A \cup C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5\}\)[/tex]
4. [tex]\( A \cap B \)[/tex] [tex]$\square$[/tex] [tex]\(\{2, 4\}\)[/tex]
5. [tex]\( A \cup B \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex]
Now, you can fill in the blanks based on this matching:
1. [tex]\( B \cap C \)[/tex] [tex]$\square$[/tex] null (empty set)
2. [tex]\( A \cap C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 3, 5\}\)[/tex]
3. [tex]\( A \cup C \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5\}\)[/tex]
4. [tex]\( A \cap B \)[/tex] [tex]$\square$[/tex] [tex]\(\{2, 4\}\)[/tex]
5. [tex]\( A \cup B \)[/tex] [tex]$\square$[/tex] [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.