Let X = {s, t, u, 8, 9, 10), Y = {t, v, w, 8, 10, 12), and Z= {t, v, 9, 10, 12). List the members of the given set, using set braces. XU (YNZ) (Type a list of letters and integers.)
Let X = {s, t, u, 8, 9, 10), Y = {t, v, w, 8, 10, 12), and Z= {t, v, 9, 10, 12). List the members of the given set, using set braces. XU (YNZ) (Type a list of letters and integers.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let X = {s, t, u, 8, 9, 10}, Y = {t, v, w, 8, 10, 12}, and Z = {t, v, 9, 10, 12}. List the members of the given set, using set braces.
\( X \cup (Y \cap Z) \)
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Diagram: The image shows a space to input the answer, indicated by an icon followed by text "(Type a list of letters and integers.)".
To solve the set operation:
1. **Find the Intersection \( Y \cap Z \):** Identify common elements in sets Y and Z.
- Y = {t, v, w, 8, 10, 12}
- Z = {t, v, 9, 10, 12}
- Intersection: \( Y \cap Z = \{t, v, 10, 12\} \)
2. **Find the Union \( X \cup (Y \cap Z) \):** Combine the elements in set X with the intersection.
- X = {s, t, u, 8, 9, 10}
- Union: \( X \cup \{t, v, 10, 12\} = \{s, t, u, 8, 9, 10, v, 12\} \)
Final Result: \{s, t, u, 8, 9, 10, v, 12\}
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