### Properties of Divisibility#### Proposition 1.4:**Let \(a, b, c \in \mathbb{Z}\). Use the definition of divisibility to directly prove the following properties of divisibility:**(a) If \(a \mid b\) and \(b \mid c\), then \(a \mid c\).(b) If \(a \mid b\) and \(b \mid a\), then \(a = \pm b\).(c) If \(a \mid b\) and \(a \mid c\), then \(a \mid (b + c)\) and \(a \mid (b - c)\).

Answered: .6. Let a, b, c € Z. Use the definition…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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.6. Let a, b, c € Z. Use the definition of divisibility to directly prove the following roperties of divisibility. (This is Proposition 1.4.) [a) If a | b and b | c, then a | c. b) If a | b and b|a, then a = ±b. c) If a b and a | c, then a (b + c) and a | (b − c).