weche relationen sind "well founded" relations?

Question

Aufgabe:

Text erkannt:

b) Which of the following relations is well-founded? Give a justification of why or why not.
i) A relation that is irreflexive, asymmetric, and finite.
ii) The relation $R=\{(n-1, n) \mid n \in \mathbb{N}\}$.
iii) The relation $R R$, where $\mathrm{R}$ is defined as above.
iv) The partial order on $\mathbb{N} \times \mathbb{N}$ where $(a, b) \preceq(c, d)$ iff $\max (a, b) \leq \max (c, d)$.
v) The divisibility order on $\mathbb{N}$, i.e. $R=\{(a, b) \mid a, b \in \mathbb{Z}$ and $\exists c(c \in \mathbb{Z} \wedge a \cdot c=b)\}$.
vi) The relation $\left\{(u a b v, u b a v) \mid u, v \in\{a, b, c\}^{*}\right\}$; that is, two words $w$ and $w^{\prime}$ are related if we can obtain $w^{\prime}$ from $w$ by replacing one occurrence of the subword $a b$ with $b a$.

Problem/Ansatz:

kann mir hier wer weiterhelfen ob diese Relationen well founded sind und warum?