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For each of the following statements, if the statement is true, then give a proof, and if the statement is false, then write out its negation and prove that. (a) For all sets A, B and C, AU (BOC) is a subset of (AUB) n(AUC). (b) For all sets A, B and C, if ACB, then (C-A) ≤ (C - B). (c) For all sets A, B and C, (AUB) - C = (A-C) U (B-C). (d) For all sets A and B, ACB if and only if A - B = 0.

For each of the following statements, if the statement is true, then give a proof, and if the statement is false, then write out its negation and prove that. (a) For all sets A, B and C, AU (BOC) is a subset of (AUB) n(AUC). (b) For all sets A, B and C, if ACB, then (C-A) ≤ (C - B). (c) For all sets A, B and C, (AUB) - C = (A-C) U (B-C). (d) For all sets A and B, ACB if and only if A - B = 0.

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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For each of the following statements, if the statement is true, then give a proof, and if the statement is false, then write out its negation and prove that. (a) For all sets A, B and C, AU (BOC) is a subset of (AUB) n(AUC). (b) For all sets A, B and C, if ACB, then (C-A) ≤ (C - B). (c) For all sets A, B and C, (AUB) - C = (A-C) U (B-C). (d) For all sets A and B, ACB if and only if A - B = 0.
Transcribed Image Text:For each of the following statements, if the statement is true, then give a proof, and if the statement is false, then write out its negation and prove that. (a) For all sets A, B and C, AU (BOC) is a subset of (AUB) n(AUC). (b) For all sets A, B and C, if ACB, then (C-A) ≤ (C - B). (c) For all sets A, B and C, (AUB) - C = (A-C) U (B-C). (d) For all sets A and B, ACB if and only if A - B = 0.
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