Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the union of two sets [tex]\(X\)[/tex] and [tex]\(Y\)[/tex], we'll follow these steps:
1. Identify the elements of each set:
- Set [tex]\(X\)[/tex] is given as [tex]\(\{a, b, c\}\)[/tex].
- Set [tex]\(Y\)[/tex] is given as [tex]\(\{0\}\)[/tex].
2. Understand the Union operation:
The union of two sets [tex]\(X\)[/tex] and [tex]\(Y\)[/tex], denoted as [tex]\(X \cup Y\)[/tex], is a set containing all elements that are in [tex]\(X\)[/tex], or in [tex]\(Y\)[/tex], or in both. Each element is included only once regardless of how many times it appears in the original sets.
3. Combine the elements:
We now combine all distinct elements from both sets:
- From set [tex]\(X\)[/tex]: [tex]\(a, b, c\)[/tex]
- From set [tex]\(Y\)[/tex]: [tex]\(0\)[/tex]
4. Form the union:
Combine all distinct elements into one set. Since none of the elements in set [tex]\(X\)[/tex] is in set [tex]\(Y\)[/tex], all elements are included exactly once.
Hence, the union [tex]\(X \cup Y\)[/tex] is:
[tex]\[ X \cup Y = \{ a, b, c, 0 \} \][/tex]
Therefore, the union of sets [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] is [tex]\(\{a, b, c, 0\}\)[/tex].
1. Identify the elements of each set:
- Set [tex]\(X\)[/tex] is given as [tex]\(\{a, b, c\}\)[/tex].
- Set [tex]\(Y\)[/tex] is given as [tex]\(\{0\}\)[/tex].
2. Understand the Union operation:
The union of two sets [tex]\(X\)[/tex] and [tex]\(Y\)[/tex], denoted as [tex]\(X \cup Y\)[/tex], is a set containing all elements that are in [tex]\(X\)[/tex], or in [tex]\(Y\)[/tex], or in both. Each element is included only once regardless of how many times it appears in the original sets.
3. Combine the elements:
We now combine all distinct elements from both sets:
- From set [tex]\(X\)[/tex]: [tex]\(a, b, c\)[/tex]
- From set [tex]\(Y\)[/tex]: [tex]\(0\)[/tex]
4. Form the union:
Combine all distinct elements into one set. Since none of the elements in set [tex]\(X\)[/tex] is in set [tex]\(Y\)[/tex], all elements are included exactly once.
Hence, the union [tex]\(X \cup Y\)[/tex] is:
[tex]\[ X \cup Y = \{ a, b, c, 0 \} \][/tex]
Therefore, the union of sets [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] is [tex]\(\{a, b, c, 0\}\)[/tex].
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.