698 views
The set of all English words ordered in a dictionary is ________

$A)$ not a poset

$B)$ a poset but not totally ordered

$C)$ a totally ordered set but not well ordered

$D)$ a well ordered set

we can compare each word with another word with the property of Lexographical Order

∴ it is as (A,≤) ====> it is a poset

and every element is comparable with other ===> it is Totally Order.

it have lower bond ===> it is Well-ordered

A total order is a partial order $\subset A \times A$ where

$\forall x$ϵA $\forall y$ϵA ($xRy \vee yRx$)