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(Exploration 1) Which of the following statements are true? (a, b, and c are integers, not nec- essarily positive.) Give informal explanations of your answers. a) If a b and b|c, then a c. b) If a b and a c, then a (b + c). c) If alc and blc, then (ab)|c.

(Exploration 1) Which of the following statements are true? (a, b, and c are integers, not nec- essarily positive.) Give informal explanations of your answers. a) If a b and b|c, then a c. b) If a b and a c, then a (b + c). c) If alc and blc, then (ab)|c.

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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1. (Exploration 1) Which of the following statements are true? (a, b, and c are integers, not nec- essarily positive.) Give informal explanations of your answers. a) If a b and b|c, then a c. b) If a b and a c, then a (b + c). c) If a c and blc, then (ab)|c. d) If a b and cld, then (ac)| (bd). e) If a b and cld, then (a + c)(b + d).
Transcribed Image Text:1. (Exploration 1) Which of the following statements are true? (a, b, and c are integers, not nec- essarily positive.) Give informal explanations of your answers. a) If a b and b|c, then a c. b) If a b and a c, then a (b + c). c) If a c and blc, then (ab)|c. d) If a b and cld, then (ac)| (bd). e) If a b and cld, then (a + c)(b + d).
Expert Solution
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As per our company guidelines, we are supposed to answer only the first three subparts of the question. Kindly repost the other parts in the next question.

Let us suppose that a,b and c are integers where a≠0 and b≠0.

We know that, x|y means x divides y.

In other words, y is a multiple of x.

If x|y, then there exists some integer k such that y=kx (By the definition of divisibility).

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