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Prove each of the following statements by using a direct proof, a proof by contrapositive, or a proof by contradiction (and cases when needed). Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. You must write down all proofs in acceptable mathematical language: make sure that you mark the beginning and end of the proof, state every assumption, define every variable, give a justification for every assertion (e.g., by the definition of...), and use complete, grammatically correct sentences. 1. For any integer n, if 7n – 3 is even, then ʼn is odd. 2. For any real number x, x-6] + x > 3.

Prove each of the following statements by using a direct proof, a proof by contrapositive, or a proof by contradiction (and cases when needed). Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. You must write down all proofs in acceptable mathematical language: make sure that you mark the beginning and end of the proof, state every assumption, define every variable, give a justification for every assertion (e.g., by the definition of...), and use complete, grammatically correct sentences. 1. For any integer n, if 7n – 3 is even, then ʼn is odd. 2. For any real number x, x-6] + x > 3.

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 each of the following statements by using a direct proof, a proof by contrapositive, or a proof by contradiction (and cases when needed). Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. You must write down all proofs in acceptable mathematical language: make sure that you mark the beginning and end of the proof, state every assumption, define every variable, give a justification for every assertion (e.g., by the definition of...), and use complete, grammatically correct sentences. 1. For any integer n, if 7n – 3 is even, then ʼn is odd. 2. For any real number x, x-6] + x > 3.
Transcribed Image Text:Prove each of the following statements by using a direct proof, a proof by contrapositive, or a proof by contradiction (and cases when needed). Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. You must write down all proofs in acceptable mathematical language: make sure that you mark the beginning and end of the proof, state every assumption, define every variable, give a justification for every assertion (e.g., by the definition of...), and use complete, grammatically correct sentences. 1. For any integer n, if 7n – 3 is even, then ʼn is odd. 2. For any real number x, x-6] + x > 3.
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