Math Help - relations

1. relations

Looking for some help with this problem, Thanks ahead of time

. Given the relation defined on N XN by (a, b) "<" (c, d) iff b < d.
(a). Why is the relation well-founded?

(b). What are the minimal elements?

2. Hello,

This relation is well-founded if there doesn't exist an infinite sequence ( $x_n$) such as $(a, x_{n+1})<(a, x_n)$

Assuming that it's not well-founded, this means that there will always be $x \in \mathbb{N}$ such as $x

If $x_n=0$, it's a nonsense since there doesn't exist such an x.

Hence, the relation is well-founded...

Minimal elements will be any elements such as $(a_m,b_m)<(c,d) \ , \ \forall c, \ d \in \mathbb{N}$

This means that $a_m$ can be any element in $\mathbb{N}$

$b_m$ has to be the element such as $\forall d \in \mathbb{N}$, $b_m

So logically, $b_m=0$ but I think there is a problem