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T T T T F 18. Let A and B be sets then A + B if, and only if A ¢ B and B ¢ A. For sets A, B, and C, if An B = AN C, then B = C. F 19. F 20. For sets A, B, and C, A U (BNC) = (A U B) N (A U C). For sets A, B, and C, A U (BU C) = (AUB) U C. F 21.

T T T T F 18. Let A and B be sets then A + B if, and only if A ¢ B and B ¢ A. For sets A, B, and C, if An B = AN C, then B = C. F 19. F 20. For sets A, B, and C, A U (BNC) = (A U B) N (A U C). For sets A, B, and C, A U (BU C) = (AUB) U C. F 21.

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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**Transcription of Set Theory Concepts:** 1. **Statement 18:** - Let A and B be sets. A is not equal to B, if and only if, A is not a subset of B and B is not a subset of A. 2. **Statement 19:** - For sets A, B, and C, if \( A \cap B = A \cap C \), then B equals C. 3. **Statement 20:** - For sets A, B, and C, the union of A with the intersection of B and C, i.e., \( A \cup (B \cap C) \), is equal to the intersection of the union of A and B with the union of A and C, i.e., \( (A \cup B) \cap (A \cup C) \). 4. **Statement 21:** - For sets A, B, and C, the union of A with the union of B and C, i.e., \( A \cup (B \cup C) \), is equal to the union of the union of A and B with C, i.e., \( (A \cup B) \cup C \). Each statement is labeled as either true or false, based on its correctness in mathematical set theory.
Transcribed Image Text:**Transcription of Set Theory Concepts:** 1. **Statement 18:** - Let A and B be sets. A is not equal to B, if and only if, A is not a subset of B and B is not a subset of A. 2. **Statement 19:** - For sets A, B, and C, if \( A \cap B = A \cap C \), then B equals C. 3. **Statement 20:** - For sets A, B, and C, the union of A with the intersection of B and C, i.e., \( A \cup (B \cap C) \), is equal to the intersection of the union of A and B with the union of A and C, i.e., \( (A \cup B) \cap (A \cup C) \). 4. **Statement 21:** - For sets A, B, and C, the union of A with the union of B and C, i.e., \( A \cup (B \cup C) \), is equal to the union of the union of A and B with C, i.e., \( (A \cup B) \cup C \). Each statement is labeled as either true or false, based on its correctness in mathematical set theory.
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