Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Let's analyze each part separately and match them correctly.
1. [tex]\(D \cap E\)[/tex]: This is the set of elements that are in both [tex]\(D\)[/tex] (whole numbers from 0 to 100) and [tex]\(E\)[/tex] (perfect squares less than 100).
[tex]\[ D \cap E = \{0, 1, 4, 9, 16, 25, 36, 49, 64, 81\} \][/tex]
2. [tex]\(D \cap F\)[/tex]: This is the set of elements that are in both [tex]\(D\)[/tex] (whole numbers from 0 to 100) and [tex]\(F\)[/tex] (even numbers between 10 and 20).
[tex]\[ D \cap F = \{10, 12, 14, 16, 18\} \][/tex]
3. [tex]\(D \cap (E \cap F)\)[/tex]: First, we find [tex]\(E \cap F\)[/tex], which is the set of elements that are both perfect squares less than 100 and even numbers between 10 and 20.
- [tex]\(E \cap F = \{16\}\)[/tex]
Then we take the intersection of this set with [tex]\(D\)[/tex]:
[tex]\[ D \cap (E \cap F) = \{16\} \][/tex]
4. [tex]\(D \cup (E \cap F)\)[/tex]: Using the same [tex]\(E \cap F\)[/tex] from above:
[tex]\[ D \cup (E \cap F) = \text{All whole numbers from 0 to 100} \cup \{16\} = \text{All whole numbers from 0 to 100} \][/tex]
5. [tex]\(D \cap (E \cup F)\)[/tex]: First, we find [tex]\(E \cup F\)[/tex], which is the set of elements that are either perfect squares less than 100 or even numbers between 10 and 20:
- [tex]\(E \cup F = \{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\}\)[/tex]
Then we take the intersection of this set with [tex]\(D\)[/tex]:
[tex]\[ D \cap (E \cup F) = \{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\} \][/tex]
Matching the answers to their respective options:
1. [tex]\(D \cap E\)[/tex] matches [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81\}\)[/tex].
2. [tex]\(D \cap F\)[/tex] matches [tex]\(\{10, 12, 14, 16, 18\}\)[/tex].
3. [tex]\(D \cap (E \cap F)\)[/tex] matches [tex]\(16\)[/tex].
4. [tex]\(D \cup (E \cap F)\)[/tex] matches "all whole numbers".
5. [tex]\(D \cap (E \cup F)\)[/tex] matches [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\}\)[/tex].
Therefore, the correctly completed matching is:
1. [tex]\(D \cap E\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81\}\)[/tex]
2. [tex]\(D \cap F\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{10, 12, 14, 16, 18\}\)[/tex]
3. [tex]\(D \cap (E \cap F)\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{16\}\)[/tex]
4. [tex]\(D \cup (E \cap F)\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\text{All whole numbers}\)[/tex]
5. [tex]\(D \cap (E \cup F)\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\}\)[/tex]
1. [tex]\(D \cap E\)[/tex]: This is the set of elements that are in both [tex]\(D\)[/tex] (whole numbers from 0 to 100) and [tex]\(E\)[/tex] (perfect squares less than 100).
[tex]\[ D \cap E = \{0, 1, 4, 9, 16, 25, 36, 49, 64, 81\} \][/tex]
2. [tex]\(D \cap F\)[/tex]: This is the set of elements that are in both [tex]\(D\)[/tex] (whole numbers from 0 to 100) and [tex]\(F\)[/tex] (even numbers between 10 and 20).
[tex]\[ D \cap F = \{10, 12, 14, 16, 18\} \][/tex]
3. [tex]\(D \cap (E \cap F)\)[/tex]: First, we find [tex]\(E \cap F\)[/tex], which is the set of elements that are both perfect squares less than 100 and even numbers between 10 and 20.
- [tex]\(E \cap F = \{16\}\)[/tex]
Then we take the intersection of this set with [tex]\(D\)[/tex]:
[tex]\[ D \cap (E \cap F) = \{16\} \][/tex]
4. [tex]\(D \cup (E \cap F)\)[/tex]: Using the same [tex]\(E \cap F\)[/tex] from above:
[tex]\[ D \cup (E \cap F) = \text{All whole numbers from 0 to 100} \cup \{16\} = \text{All whole numbers from 0 to 100} \][/tex]
5. [tex]\(D \cap (E \cup F)\)[/tex]: First, we find [tex]\(E \cup F\)[/tex], which is the set of elements that are either perfect squares less than 100 or even numbers between 10 and 20:
- [tex]\(E \cup F = \{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\}\)[/tex]
Then we take the intersection of this set with [tex]\(D\)[/tex]:
[tex]\[ D \cap (E \cup F) = \{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\} \][/tex]
Matching the answers to their respective options:
1. [tex]\(D \cap E\)[/tex] matches [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81\}\)[/tex].
2. [tex]\(D \cap F\)[/tex] matches [tex]\(\{10, 12, 14, 16, 18\}\)[/tex].
3. [tex]\(D \cap (E \cap F)\)[/tex] matches [tex]\(16\)[/tex].
4. [tex]\(D \cup (E \cap F)\)[/tex] matches "all whole numbers".
5. [tex]\(D \cap (E \cup F)\)[/tex] matches [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\}\)[/tex].
Therefore, the correctly completed matching is:
1. [tex]\(D \cap E\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81\}\)[/tex]
2. [tex]\(D \cap F\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{10, 12, 14, 16, 18\}\)[/tex]
3. [tex]\(D \cap (E \cap F)\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{16\}\)[/tex]
4. [tex]\(D \cup (E \cap F)\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\text{All whole numbers}\)[/tex]
5. [tex]\(D \cap (E \cup F)\)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(\{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 12, 14, 18\}\)[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
