Recall that a |b is a relation on the natural numbers meaning “a divides b.” It is defined by a |b ≡(∃c ∈N)(a ·c = b). 4. Similarly, if c | a and c | b, must c | a + b? Either give a counterexample or prove (∀a, b, c ∈N)(c |a →(c |b →c |(a + b))).

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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Question

Recall that a |b is a relation on the natural numbers meaning “a divides
b.” It is defined by a |b ≡(∃c ∈N)(a ·c = b).

4. Similarly, if c | a and c | b, must c | a + b? Either give a counterexample

or prove
(∀a, b, c ∈N)(c |a →(c |b →c |(a + b))).

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