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
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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.

\( X \cup (Y \cap Z) \)

---

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\}
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. \( X \cup (Y \cap Z) \) --- 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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