The transitive law states that:

For real numbers $a$, $b$ and $c$:

$a<b \text{ and } b<c \Rightarrow a<c$

I am not sure how to apply it in the following cases ($x \in \mathbb{R}$):

1. $a \le x \text{ and } x \le b$
2. $a \le x \text{ and } x \lt b$
3. $a \lt x \text{ and } x \le b$

After doing some exercises, it seems that the answer is as follows:

1. $a \le b$
2. $a \lt b$
3. $a \lt b$

I don't know how to apply the transitive law to arrive at the answer. My solution was $a \le b$ for all 3 cases as I thought that would account for the cases where $a<b$ and/or $a=b$