2 votes
2 votes
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
in Set Theory & Algebra
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2 Comments

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

about Well-order information https://en.wikipedia.org/wiki/Well-order

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

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