Question

Prove that (a) if $a|b$ and $b|c$ then $a|c$; (b) if $a|b$ and $c|d$ then $ac|bd$; (c) if $m eq 0$, then $a|b$ if and only if $ma|mb$; (d) if $d|a$ and $a eq 0$ then $|d| leq |a|$.

          Prove that
(a) if $a|b$ and $b|c$ then $a|c$;
(b) if $a|b$ and $c|d$ then $ac|bd$;
(c) if $m 
eq 0$, then $a|b$ if and only if $ma|mb$;
(d) if $d|a$ and $a 
eq 0$ then $|d| leq |a|$.

Added by Tyler B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ankit Gupta

04/21/2020

Step 1

Let's assume $a = x$, $b = x + y$, and $c = x + y + z$ where $x$, $y$, and $z$ are positive numbers. Given $a < b$, we have $x < x + y$ which implies $y > 0$. Given $b < c$, we have $x + y < x + y + z$ which implies $z > 0$. Show more…

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