Let R 1 and R 2 be relations on N defined by
xR 1 y if and only if y=a+x for some a∈N 0 .
xR 2 y if and only if y=xa for some a∈N
For all x;y∈N.
Also N 0 denotes all integers x≥0 , while N denotes all integers x≥1 .
There are two different things I want to prove with this.
I want to write a proof to show that R 1 is a partial order on N .
I want to write a proof to show that R 2 is a partial order on N .
I have others that I want to try and do but for now if someone could model how to write a proof for these that would be great as I could reference to it.