My question may seem a bit strange, but I asked it anyway.
Suppose two orders sets. $A$ and $B$ and $A\cap B=\emptyset$. Is $A\cup B$ an order set?
A concrete case : suppose $A=\{0,1\}$ with the order $0<1$ and $B=\{2,3\}$ with $3<2$. Is $A\cup B$ an order set?
If i want $A\cup B$ to be an order set systematically what condition do I have to apply on $A$ and $B$
Thank you