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(a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c) For all real numbers a and b, if a < b then 4ab < (a + b)².

(a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c) For all real numbers a and b, if a < b then 4ab < (a + b)².

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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Prove or disprove each of the following statements. Some statements are true, but some are false. For each one, either provide a proof to verify the statement is true, or find a counterexample to establish that the claim is false.
Transcribed Image Text:Prove or disprove each of the following statements. Some statements are true, but some are false. For each one, either provide a proof to verify the statement is true, or find a counterexample to establish that the claim is false.
(a) For every integer n, the number n² (b) For all real numbers a, a² < aª. (c) For all real numbers a and b, if a < b then 4ab < (a + b)². n must be even.
Transcribed Image Text:(a) For every integer n, the number n² (b) For all real numbers a, a² < aª. (c) For all real numbers a and b, if a < b then 4ab < (a + b)². n must be even.
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