Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
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 time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
