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11. For sets A and B, define AAB (A\B) U (B\A). Prove that A B if and only if AAB=0. - (a) Let A and B be sets. (b) Let A and B be sets. Prove that AAB=BAA. (c) Let A, B, and C be sets. Prove that (AAB) AC = AA (BAC).

11. For sets A and B, define AAB (A\B) U (B\A). Prove that A B if and only if AAB=0. - (a) Let A and B be sets. (b) Let A and B be sets. Prove that AAB=BAA. (c) Let A, B, and C be sets. Prove that (AAB) AC = AA (BAC).

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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11. For sets A and B, define AAB (A\B) U (B\A). (a) Let A and B be sets. Prove that A = B if and only if AAB = 0. (b) Let A and B be sets. Prove that AAB = BAA. (c) Let A, B, and C be sets. Prove that (AAB) AC = AA (BAC).
Transcribed Image Text:11. For sets A and B, define AAB (A\B) U (B\A). (a) Let A and B be sets. Prove that A = B if and only if AAB = 0. (b) Let A and B be sets. Prove that AAB = BAA. (c) Let A, B, and C be sets. Prove that (AAB) AC = AA (BAC).
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