Inverse relation of $x<y$ defined on $\mathbb N$

Question

The relation is this: $R=\{(a,b):a<b\}$ on $\mathbb{N}$. How do I find an inverse of this relation?

I can see that it is $R^{-1}=\{(a,b):b<a\}$ but I do not know how to prove it. Can someone help me out?

Answer 1

$R^{-1}=\{(x,y)\in \mathbb{N}\times\mathbb{N}:(y,x)\in R\}$

=$\{(x,y)\in \mathbb{N}\times\mathbb{N}:(y,x)\in \{(a,b):a<b\}\}$

=$\{(x,y)\in \mathbb{N}\times\mathbb{N}:y<x\}$

and change the letters.