Let U = {1,5,7,8,10,13,15,17,18). Determine the complement of the set (5,7,10,15,18).
Let U = {1,5,7,8,10,13,15,17,18). Determine the complement of the set (5,7,10,15,18).
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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![**Set Theory: Understanding Complements**
**Problem Statement:**
Given the universal set \( U = \{1, 5, 7, 8, 10, 13, 15, 17, 18\} \), determine the complement of the set \( \{5, 7, 10, 15, 18\} \).
**Solution:**
The complement of a set \( A \) with respect to a universal set \( U \) includes all the elements that are in \( U \) but not in \( A \).
**Steps to find the complement:**
1. Identify the universal set \( U \).
2. Identify the set \( A \) for which the complement is being determined.
3. Subtract the elements of \( A \) from \( U \).
**Given Data:**
- Universal set \( U = \{1, 5, 7, 8, 10, 13, 15, 17, 18\} \)
- Set \( A = \{5, 7, 10, 15, 18\} \)
**Complement Calculation:**
Find all elements in \( U \) that are not in \( A \):
- Elements in \( U \): 1, 5, 7, 8, 10, 13, 15, 17, 18
- Elements in \( A \): 5, 7, 10, 15, 18
Elements in \( U \) but not in \( A \): 1, 8, 13, 17
**Result:**
The complement of the set \( \{5, 7, 10, 15, 18\} \) is:
\[ \{1, 8, 13, 17\} \]
**Instructions for Students:**
- Write the answers separated by commas.
- Ensure the elements are in ascending order.
**Example Answer:**
The complement is \( \{1, 8, 13, 17\} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc0fe995-7680-4da1-9251-6315116f8ff1%2F9abb1d1f-59ad-4df6-b2bd-1d1f8a96d483%2Fgl1t9f8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Set Theory: Understanding Complements**
**Problem Statement:**
Given the universal set \( U = \{1, 5, 7, 8, 10, 13, 15, 17, 18\} \), determine the complement of the set \( \{5, 7, 10, 15, 18\} \).
**Solution:**
The complement of a set \( A \) with respect to a universal set \( U \) includes all the elements that are in \( U \) but not in \( A \).
**Steps to find the complement:**
1. Identify the universal set \( U \).
2. Identify the set \( A \) for which the complement is being determined.
3. Subtract the elements of \( A \) from \( U \).
**Given Data:**
- Universal set \( U = \{1, 5, 7, 8, 10, 13, 15, 17, 18\} \)
- Set \( A = \{5, 7, 10, 15, 18\} \)
**Complement Calculation:**
Find all elements in \( U \) that are not in \( A \):
- Elements in \( U \): 1, 5, 7, 8, 10, 13, 15, 17, 18
- Elements in \( A \): 5, 7, 10, 15, 18
Elements in \( U \) but not in \( A \): 1, 8, 13, 17
**Result:**
The complement of the set \( \{5, 7, 10, 15, 18\} \) is:
\[ \{1, 8, 13, 17\} \]
**Instructions for Students:**
- Write the answers separated by commas.
- Ensure the elements are in ascending order.
**Example Answer:**
The complement is \( \{1, 8, 13, 17\} \).
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