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Let n is a positive integer. Prove that n is even if and only if 7n+4 is even. (Hint: you must prove bi-implication, it means p-q = (p¬q) ^ (q-p).) Let m, n are integers. Prove that if m*n is even, then m is even or n is even. Specify what type of proof you are using.

Let n is a positive integer. Prove that n is even if and only if 7n+4 is even. (Hint: you must prove bi-implication, it means p-q = (p¬q) ^ (q-p).) Let m, n are integers. Prove that if m*n is even, then m is even or n is even. Specify what type of proof you are using.

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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Let n is a positive integer. Prove that n is even if and only if 7n+4 is even. (Hint: you must prove bi-implication, it means p-q = (p¬q) ^ (q-p).) Let m, n are integers. Prove that if m*n is even, then m is even or n is even. Specify what type of proof you are using.
Transcribed Image Text:Let n is a positive integer. Prove that n is even if and only if 7n+4 is even. (Hint: you must prove bi-implication, it means p-q = (p¬q) ^ (q-p).) Let m, n are integers. Prove that if m*n is even, then m is even or n is even. Specify what type of proof you are using.
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