Let $D=\{14,17,19\}, E=\{14,16,17,18\}$ and $F=\{13,15,16,17,19\}$. List the elements in the set $D \cup E$.
$D \cup E=$ $\square$ (Use commas to separate answers.)
Answer (2)
List elements of set D: 14, 17, 19.
List elements of set E: 14, 16, 17, 18.
Combine elements, removing duplicates: 14, 16, 17, 18, 19.
Write the final set in ascending order: { 14 , 16 , 17 , 18 , 19 } . The union of D and E is { 14 , 16 , 17 , 18 , 19 } .
Explanation
Understanding the Problem We are given two sets, D = { 14 , 17 , 19 } and E = { 14 , 16 , 17 , 18 } . We need to find the union of these two sets, which means we need to combine all the elements from both sets into a single set, removing any duplicates.
Listing Elements from Set D First, let's list all the elements from set D: 14, 17, 19.
Listing Elements from Set E Next, let's list all the elements from set E: 14, 16, 17, 18.
Combining the Elements Now, let's combine the two lists, removing any duplicate elements. The combined list is: 14, 16, 17, 18, 19.
Writing the Final Set Finally, we write the resulting set in ascending order: { 14 , 16 , 17 , 18 , 19 } .
Examples
Understanding set operations like union is fundamental in many areas, including database management and data analysis. For example, imagine you have two lists of customers: one list of customers who purchased product A and another list of customers who purchased product B. Finding the union of these two sets would give you a list of all customers who purchased either product A or product B or both. This information can be useful for marketing campaigns or product development strategies.
The union of sets D and E is D ∪ E = { 14 , 16 , 17 , 18 , 19 } . This is obtained by combining all unique elements from both sets and removing duplicates. The final result is expressed in ascending order.
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