Let $D=\{6,9,11\}, E=\{6,8,9,10\}$ and $F=\{5,7,8,9,11\}$. List the elements in the set $D \cup E$.
$DUE = \square$ (Use commas to separate answers.)
Answer (1)
List elements of set D: D = { 6 , 9 , 11 } .
List elements of set E: E = { 6 , 8 , 9 , 10 } .
Combine the elements, removing duplicates: D ∪ E = { 6 , 8 , 9 , 10 , 11 } .
The union of D and E is { 6 , 8 , 9 , 10 , 11 } .
Explanation
Understanding the Problem We are given two sets, D = { 6 , 9 , 11 } and E = { 6 , 8 , 9 , 10 } . We need to find the union of these two sets, which means we need to list all the elements that are in either set D or set E or in both.
Listing the Elements The elements in set D are 6, 9, and 11. The elements in set E are 6, 8, 9, and 10.
Combining the Sets To find the union D ∪ E , we combine the elements of both sets, but we only list each element once, even if it appears in both sets. So, we have the elements 6, 9, 11 from set D , and 6, 8, 9, 10 from set E . Combining these and removing duplicates, we get the set { 6 , 8 , 9 , 10 , 11 } .
Final Answer Therefore, D ∪ E = { 6 , 8 , 9 , 10 , 11 } .
Examples
Understanding set operations like union is fundamental in many areas, such as database management, where you might want to combine customer lists from different sources, or in network analysis, where you might want to identify all the nodes connected to at least one of two subnetworks. For instance, if you have two groups of friends, set operations help you find all the people in either group without listing anyone twice. This concept is also used in search engines to combine results from different search queries, ensuring a comprehensive list of relevant information. In essence, set union helps in consolidating information and resources efficiently.
