Originally Posted by

**mj2323** 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.

1.

I want to write a proof to show that R 1 is a partial order on N .

2.

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.