(a)This is not a wellordered set. For example, (0, 1) has no minimal element. Suppose that x is minimal, then we can find some \(\displaystyle{0}{<}{y}{<}=\), and so \(\displaystyle{y}€{\left({0},{1}\right)}\) but y (b)This is similar to (a) — (0,1) has no maximal (<-minimal) element.

(c)This set has no minimal element so it cannot be well-ordered.

(a)This is a. well ordered set. Denote this set by S. Denote by 5. the set

S = {0,1,2,....4}

Let T he somenonempty subset of S. We must prove that 7 has a minimal element.

First of all, \(\displaystyle{T}={\left\lbrace{S}{\mid}{i}∈{T}\right\rbrace}\),

where \(\displaystyle{T}⊆{N}.\) Since \({T}⊆{N}\)and N is well-ordered, it has a minimal element in. Now we see that

\(\displaystyle{S}{i}_{0}∈{T}\) and \(\displaystyle{T}⊆{S}{i}_{0},{T}∈{T}\)

so Si0 is a minimal element of T.