Chapter 4.2, Problem 10E

To determine

Whether the statements given below are true or false. Justify your answer with a proof or a counterexample.

1. If $a|b$ and $b|\left(-c\right)$, then $a|c$.

2. If $a|b$ and $c|b$, then $ac|b$.

3. If $a|b$ and $a|c$, then $a|bc$.

4. If $a|b$ and $c|d$, then $ac|bd$.

5. If $a|b$ and $c|\frac{b}{a}$, then $c|b$ and $a|\frac{b}{c}$.