True or false questions about divisibility and non-divisibility in the integers. I'm confused.

Question

For $a$, $b$, c $\in \mathbb{Z}$.

True or false that:

1. If $a$ doesn't divide $b$ and $b$ doesn't divide $c$ then $a$ doesn't divide $c$

2. If $a$<$b$ then $a$ divide $b$

3. If $a$ doesn't divide $b$ and $b$ doesn't divide $c$ then $a$ doesn't divide $b+c$

4. If $a$ divide $b$ and $b$ divide $a$ then $a$=$b$

I'm very confused about divisibility and non-divisibility

Answer 1

1. False. E.g. $a = 3, b = 4, c = 6$. Meanwhile if the "doesn't" changes to "does" then the statement becomes True.
2. False. E.g. $a = 3, b = 4$. Meanwhile if $a$ divides $b$ then $a \leq b$ ($a = b$ is okay).
3. False. E.g. $a = 3, b = 4, c = 5$.
4. False if either $a$ or $b$ can be negative, but if both must be positive or negative at the same time then True. This depends on the definition of "divisor" you need.