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Q1: Let A= {1,2,5,7}, B= {2,7,8}, U = {1,2,3,4,5,6,7,8} 1) A UB 2) A N B 3) ĀNB 4) Ā U Ē

Q1: Let A= {1,2,5,7}, B= {2,7,8}, U = {1,2,3,4,5,6,7,8} 1) A UB 2) A N B 3) ĀNB 4) Ā U Ē

Advanced Engineering Mathematics
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 Operations and Venn Diagrams #### Question 1: Given the following sets: - **Set A**: \( \{1, 2, 5, 7\} \) - **Set B**: \( \{2, 7, 8\} \) - **Universal Set U**: \( \{1, 2, 3, 4, 5, 6, 7, 8\} \) Evaluate the following operations: 1. **Union of A and B** (\( A \cup B \)): The union of sets A and B includes all elements that are in A, in B, or in both. 2. **Intersection of A and B** (\( A \cap B \)): The intersection of sets A and B includes only the elements that are in both A and B. 3. **Intersection of the complements of A and B** (\( \overline{A} \cap \overline{B} \)): The complement of a set A (\( \overline{A} \)) includes all elements in the universal set U that are not in A. The intersection of the complements of A and B includes all elements that are neither in A nor in B. 4. **Union of the complements of A and B** (\( \overline{A} \cup \overline{B} \)): The union of the complements of A and B includes all elements that are either not in A, not in B, or in neither. Use the universally accepted Venn diagram to help visualize these operations.
Transcribed Image Text:### Set Operations and Venn Diagrams #### Question 1: Given the following sets: - **Set A**: \( \{1, 2, 5, 7\} \) - **Set B**: \( \{2, 7, 8\} \) - **Universal Set U**: \( \{1, 2, 3, 4, 5, 6, 7, 8\} \) Evaluate the following operations: 1. **Union of A and B** (\( A \cup B \)): The union of sets A and B includes all elements that are in A, in B, or in both. 2. **Intersection of A and B** (\( A \cap B \)): The intersection of sets A and B includes only the elements that are in both A and B. 3. **Intersection of the complements of A and B** (\( \overline{A} \cap \overline{B} \)): The complement of a set A (\( \overline{A} \)) includes all elements in the universal set U that are not in A. The intersection of the complements of A and B includes all elements that are neither in A nor in B. 4. **Union of the complements of A and B** (\( \overline{A} \cup \overline{B} \)): The union of the complements of A and B includes all elements that are either not in A, not in B, or in neither. Use the universally accepted Venn diagram to help visualize these operations.
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