Doubt

Question

https://gateoverflow.in/25664/tifr2013-b-4    In this question i get it the answer is E. Plz check my reason :- 

Since its a partial order relation because:- 

we can relate every Xi << Xi   itself  and  Its antisymmetric because no such pair Xi << Xi+1 and Xi+1 << Xi can exist at the same time. Its transitive as well its easy to see. And on the other hand every dictionary order is a partial order. Its a well order because if i choose any of the sequence it will always have a least element which will relate to everyone. 

Am i correct in my justification ?

Answer 1

 In this question i get it the answer is E.

No. D will be the correct answer. Check my newly added answer on that question.  

 Its a well order because if i choose any of the sequence it will always have a least element which will relate to everyone. 

No. We won't get a least element for every Non-empty subset. For example, 

$S$ = $\left \{ a^nb\,\,|\,\,n \geq 0 \right \}$.. this Subset has No least element. Hence, The given Structure $(A, dictionary order)$ is NOT Well-Ordered Structure.